PEDAGOGICS. 


LLEN-GAINES. 


UC-NRLF 


$B  3D5  ma 


1 


PEDAGOGICS 


A  MONOGRAPH. 


A  New  Theory  and  Practice  in  Teaching. 


BY 

R.   D.  ALLEN   and  J.  T.  GAINES. 

EEEATA. 

At  bottom  of  page  28  read  "  81 "  for  "  8'." 
In  Prin.  16,  page  25,  for  "6^"  read  "a'." 


LOUISVILLE: 

PUBLISHED   BY    J.  T.   GAINES 

1889 


PEDAGOGJGS 


A  MONOGRAPH. 

t 

A  New  Theory  and  Practice  in  Teaching. 


.    BY 

R.   D.  ALLEN   and  J.  T.  GAINES. 


LOUISVILLE: 

PUBLISHED   BY    J.  T.   GAINES 
1889 


COPYRIGHTED  1889  BY 

R.  D   ALLEN  and  J.  T.  GAINES. 

SDUCATION  DEPr. 


PREFACE. 


The  authors  believe  that  in  this  little  volume  they  have 
presented  sometiiing  new  on  the  subject  of  education. 

Associated  in  normal  school  work  in  the  summer  of  1878, 
they  first  exchanged  views  upon  the  art  of  teaching.  Begin- 
ning with  substantial  agreement  in  theory  and  in  methods,  each 
has  ever  found  profit  and  pleasure  in  hearing  the  experiences 
of  the  other  in,  to  him,  a  strange  field  of  labor — the  one  being 
in  the  public  school  work,  and  the  other  in  charge  of  a  select 
private  school  for  boys. 

The  fact  observed  by  both,  that  a  method  devised  for  use 
in  one  field  could  be  successfully  applied  in  the  other,  sug- 
gested the  possibility  of  systematizing  all  teaching. 

Frequent  consultations  and  exchanges  of  experiences  with 
this  end  in  view  have  taken  place.  Many  things  have  trans- 
pired to  delay  the  accomplishment  of  their  plans.  They  do 
not  now  claim  to  have  discovered  all  or  to  have  devised  a 
perfect  system.  But  some  principles  are  now  clear  that  were 
once  dark ;  others  are  growing  clearer  as  experiment  burnishes 
them.  Enough  has  been  completed  to  justify  submitting 
their  views  to  the  great  brotherhood  of  teachers. 

They  ask  for  and  ardently  desire  criticism,  both  favorable 
and  adverse ;  the  Empire  would  not  have  been  had  no  ene- 
mies opposed  Napoleon,  nor  would  the  Lieutenant  have  been 
the  Emperor  had  no  friends  upheld  him. 

The  chief  concern  of  the  authors  has  been  to  be  under- 
stood. Pestalozzi,  Froebel,  and  Horace  Mann  were  not  under- 
stood by  their  cotemporaries,  nor  is  Parker  fully  understood 
to-day.  And  why?  No  one  can  learn  a  fad  by  reading  it  or  by 
hearing  it  unless  he  knows  it  already  in  its  elements.     It  is  by  tlie 

544290 


4  '    .  PREFACE. 

'light  of  our  experience  as  teachers  that  we  must  read  the 

words  of  a  brother.     Practical  lessons  are  given  within  these 

pages.     Begin  by  trying  these,  and  with  the  light  they  shed 

seek  to  know  the  truths  contained  herein.     That  they  are 

f  valuable  may  well  be  claimed,  for  they  are  the  assimilations 

;  from  observations  and  comparisons  upon  more  than  twenty 

(  years  of  active  school- room  work. 

The  postulates  for  teaching,  on  page  17  and  following,  were 
first  noted  down  as  indnctions  from  observations  of  work  in 
teaching.  After  they  were  agreed  upon,  a  theory  was  sought 
jthat  would  satisfy  them.  That  theory  has  been  found,  and  it 
is  the  mission  of  this  Monograph  to  expound  it.  It  is  believed 
that  it  will  satisfy  all  experiences,  from  that  of  the  mother- 
teacher  to  that  of  the  university  professor ;  that  it  will  meet 
the  wants  of  all  grades  and  kinds  of  teaching. 

No  such  absurd  claim  is  set  up  as  that  there  has  been  no 
effective  teaching  heretofore ;  it  is  only  asserted  that  often 
where  good  teaching  has  been  done  it  has  resulted  from  pur- 
suing the  line  of  least  resistance,  and  has  not  been  dictated 
by  principle. 

It  is  a  fact,  which  no  one  can  deny,  that  the  majority  of 
teachers  do  adhere  to  definitions  and  make  them  the  basis  for 
their  work. 

Believing  it  to  be  true,  that  there  is  not  a  principle  or 
truth  to  be  found  in  any  department  of  knowledge  which 
can  not  be  so  presented  that  the  pupil  shall  himself  discover 
it,  the  authors  submit  the  result  of  their  labors  to  their  col- 
leagues in  the  hope  that  many  who  are  now  working  in  dark- 
ness may  thereafter  walk  in  the  light. 

Thanks  are  due  to  Prof.  F.  E.  Spaulding,  of  Louisville 
Military  Academy,  to  Hiram  Roberts,  of  the  Louisville 
Training  School,  and  to  Messrs.  Wm.  J.  McConathy,  Wm. 
Marriner,  W.  O.  Cross,  and  O.  B.  Theiss,  of  the  Public 
Schools  of  Louisville,  for  valuable  suggestions. 

R.  D.  ALLEN, 
J.  T.  GAINES. 

Louisville,  Ky.,  November,  1889. 


THEORY. 


The  practice  of  teaching  set  forth  in  this  Monograph  is 
based  on  tlie  theory  that  "  The  primary  attributes  of  in- 
tellect are,  (1)  Consciousness  of  Differences;  (2)  Conscious- 
ness of  Agreement,  and  (3)  Ketentiveness.  Every  properly 
intellectual  function  involves  one  or  more  of  these  attributes, 
and  nothing  else."     [Bain's  Mental  Science.] 

If  it  ai)pears  that  Abstraction,  Judgment,  Reason,  Mem- 
ory, and  Imagination.*  the  so-called  faculties  of  the  Intellect, 
can  be  adequately  explained  on  this  theory,  then  it  must  be  evi- 
dent that  a  correct  practice  in  teaching  must  ever  engage  the 
powers  of  the  intellect  in  "Differences,"  in  ''Agreements," 
and  in  "  Rstentiveness,"  and  also  that  any  practice  in  teaching 
which  is  not  founded  on  the  three  attributes  mentioned  is 
wrong,  and  therefore  injurious  in  proportion  to  its  departure 
from  these  essentials  to  all  healthful  activities  of  the  intellect. 
.  No  one  can  question  the  proposition  that  agreement  of 
objects  in  qualities  is  the  foundation  of  all  classification.  This 
action  of  the  intellect  (originating  classes)  is  called  Ab.  traction 
by  some ;  by  others  it  is  called  the  Notion-forming  Power. 

Observe  the  mind  at  work  assigning  an  object  to  a  class 
already  formed.  Does  the  intellect  not  discover  the  resem- 
blance or  agreement  of  the  object  with  the  notion,  which  is 
the  basis  for  the  class  ?     Is  not  this  Judgment  f 

If  an  intellect,  without  bringing  two  objects,  A  and  B,  in 
conjunction,  perceives  their  agreement  by  virtue  of  perceived 

'•'Intelleclual  Consciousness  and  Sense  have  not  been  included  in  this  analy- 
sis of  the  faculties,  as  some  prefer,  because  they  are  conceived  to  be  merely  the 
acts  of  intellect  in  separating  objects  internal  and  external.  In  either  case,  if 
the  classification  be  retained,  the  act  named  by  the  term  is  better  expressed  by 
the  first  attribute— Consciousness  of  Differences. 


b  PEDA(lOGIt;s. 

resemblances  in  each  to  C,  with  which  it  in  turn  has  been 
compared,  and  again  discovers  agreement  in  D  and  E  by  vir- 
tue of  resemblances  in  each  to  F,  and  thus  continues  multi- 
plying its  experiences,  will  it  not  at  length  perceive  the  agree- 
ment in  these  experiences  and  be  able  to  arrive  at  the  law  : 
*'In  so  far  as  two  things  resemble  a  third  they  resemble  each 
other?"  And  is  not  this  an  exercise  of  the  intellect  in  that 
mode  of  its  existence  called  Reason  f  And  is  any  thing  else 
involved  in  the  whole  j:)rocess,  except  agreements,  differences, 
and  retentiveness? 

In  all  these  acts,  in  abstraction,  in  judgment,  and  in  rea- 
son, does  not  the  Memory  repeatedly  exhibit  itself?  What 
is  memory  if  it  be  not  a  recurrence  of  a  preceding  state  of 
the  intellect  because  of  its  agreement  or  disagreement  with  a 
present  state  ? 

Examine  the  following  product  of  the  Imagination:  "  The 
cataracts  blow  their  trumpets  from  the  steep."  What  is  it 
but  a  blending  founded  upon  the  agreement  of  the  emotions 
produced  by  the  trumpets  and  falling  waters? 

Thus  far  in  the  discussion  agreements  have  had  promi- 
nence in  reconciling  the  so-called  faculties  of  the  intellect  to 
the  theory  of  three  attributes,  and  three  alone.  But  is  not 
the  intellect  engaged  as  well  in  each  exercise  with  perception 
of  differences?  Is  not  discrimination  the  foundation  of  a 
perception  of  agreement?  Can  a  resemblance  be  perceived 
except  by  the  light  of  differences  already  perceived  ?  And 
does  not  the  intellect  after  each  exercise  retain  what  it  has 
acquired,  just  as  a  plant  retains  the  elements  it  has  stored 
from  the  air  and  earth?  ■  Could  the  intellect  abstract  without 
retaining  the  objects  to  be  compared  ?  Would  there  be  any 
thing  to  abstract  unless  they  were  thus  held  ?  Could  the  in- 
tellect judge  without  retaining  the  notion  of  the  class  as  a 
basis  with  which  to  compare  the  new  object?  Could  the  in- 
tellect make  tJie  successive  steps  required  to  reach  the  act 
known  as  reason  without  holding  over  the  fruitage  of  each 
effort  to  serve  as  the  basis  for  the  succeeding  comparison  ? 


THEORY.  7 

An  evident  corollary  of  thig  theory  is  that  a  certain  order 
must  exist  in  the  recurring  occasions  for  the  exercise  of  the 
three  attributes.  Reflection  upon  what  has  been  said  in 
respect  to  Reason  will  reveal  clearly  the  order  of  progression 
to  the  assimilation  of  any  principle. 

Observing  narrowly  an  intellect  in  its  advance  to  assimila- 
tion of  truth,  three  steps*  are  apparent,  viz:  (1)  perceiving 
objects;  (2)  distinguishing  resemblances  and  differences,  and 
(3)  discovering  the  truth  which  is  a  content  of  the  resem- 
blances. During  this  process  the  sense-objects  have  become 
thought-objects,  and  the  intellect,  retaining  only  those  parts 
which  are  essential  to  the  truth  assimilated,  perceives  the 
objects  more  clearly  than  at  first. 

Assimilated  j^f^'^^^^^P^^^  are  retained  by  the  intellect  as 
thought-objects,  and  these,  as  occasion  arises  for  an  exercise  of 
the  will  by  an  individual,  are,  (1)  perceived,  (2)  compared 
with  reference  to  their  fitness  to  the  occasion,  and  some  con- 
tent of  their  relations  (3)  taken  as  a  law  for  action. 

That  every  man  in  every  important  act  of  his  life  does 
exercise  his  intelli^ct  in  deciding  as  to  his  course  in  that  case, 
before  exercising  his  will,  can  be  illustrated  by  an  occurrence 
in  every-day  life :  One  sees  a  man  leave  his  house  prepared 
to  go  to  his  daily  work,  sees  him  pause,  look  round  carefully, 
return,  and  shortly  after  reappear  carrying  an  umbrella. 
What  has  passed  in  his  mind?  The  sultry  state  of  the 
atmosphere,  the  direction  of  the  wind,  the  distinctness  of 
sounds,  the  presence  or  absence  of  this  or  that,  many  things, 
in  fact,  which  are  retained  by  his  intellect  as  thought-objects, 
by  the  sensations  which  their  representatives  in  nature  pro- 
duce, have  aroused  his  attention.  His  intellect  at  once  insti- 
tuted a  comparison  among  them,  extending  its  view  to  embrace 
others  with  which  they  were  linked,  concerning  rain,  its  effects, 
the  value  of  life,  the  worth  of  an  umbrella  as  protection,  etc. 
From  this  comprehensive  group  his  intellect  was  able  promptly 

*  The  three  acts  of  the  intellect  here  pointed  out  will,  for  convenience, 
hereafter  in  the  text  be  called  (1)  perceiving,  (2)  comparing,  and  (3)  assimi- 
lating. 


8  PEDAGOGICS. 

to  make  a  law  for  his  guidance.  He  probably  foresaw  it 
would  be  necessary  for  him  to  be  exposed  during  the  day, 
and  he  prepared  himself. 

Suppose,  now,  that  after  pausing  and  noting  the  appear- 
ance of  things,  he  had  gone  on,  how  can  we  account  for  it? 
He  has  simply  taken  other  links  of  the  chain  as  his  law.  He 
remembers,  perhaps,  that  he  will  not  have  to  leave  his  office 
during  the  day,  and  sees  that  he  can  reach  there  before  the 
rain.  Or  perhaps  he  recalls  that  he  has  another  umbrella  at 
his  office  for  such  contingencies. 

To  illustrate  the  relations  of  these  intellect-acts,  viz., 
Perceiving,  Comparing,  and  Assimilating  to  mind  growth, 
two  simple  examples  are  here  given. 

Suppose  the  task  be  to  classify  a  number  of  marbles. 
(1)  Perceiving  takes  place.  (2)  Comparing  follows,  which 
brings  to  view  certain  resemblances,  as  color,  size,  value,  etc. 
(3)  Selection  of  one,  as  "  color,"  for  the  guiding  principle,  the 
classification  is  readily  made.  For  the  Second  illustration, 
suppose  the  task  be  to  discover  the  prii|cipl^»  upon  which 
depends  the  form  of  axle-nuts  of  a  buggy?  (1)  By  perceiv- 
ing, the  student  is  able  to  distinguish  the  nuts  and  their  pjfrts, 
viz.,  threads,  form,  motion,  orifices,  etc.,  and  also  to  dis- 
tinguish the  wheels  and  their  parts  to  which  the  nuts  are 
closely  related.  (2)  By  comparing,  he  perceives  certain  re- 
semblances, viz.,  fastenings,  covers  for  holding  grease,  which 
extend  throughout.  Persisting,  he  finds  a  resemblance  in  the 
direction  of  the  threads  in  two  of  them.  (3)  With  this 
principle  the  nuts  are  classified  as  left-handed  and  right- 
handed.  Seeking  to  reconcile  this  diflference  to  the  resem- 
blance '*  fastenings,"  he  arrives  at  the  principle. 

The  work  of  the  teacher  in  these  two  illustrations  (if  we 
impose  the  condition  of  the  learner  having  a  teacher)  would 
manifestly  be  to  let  the  mirfd  act  alone  and  for  itself  in  arriv- 
ing at  the  principle.  When  he  has  supplied  the  material,  his 
after-work  should  be  simply  to  direct  the  learner  in  his  in- 
vestigation by  proper  questions.     These  modes  of  existence 


^  THEORY.  \) 

of  the  intellect  correspond  to  the  questions  ivhat,  how,  and 
why,  and  the  teacher  is  in  his  proper  sphere  when  he  supplies 
the  stimulus  in  each  mode  indicated  by  these  interrogatories. 

The  remarkable  parallelism  in  the  three  examples  noted 
above,  in  that  the  action  of  the  intellect  in  each  is  the  same, 
leads  to  the  conclusion  that  the  acts  resulting  from  the  will 
taking  the  assimilated  truth  as  its  guide  in  each  case  are  alike 
in  kind,  and  are  therefore  phenomena  of  the  same  thing.  If 
the  acts  of  the  man  in  the  first  illustration  are  phenomena  of 
character — and  who  can  deny  that  they  are? — then,  proceed- 
ing to  classify  the  marbles  in  the  second  case,  or  doing  any 
thing  guided  by  the  truth  assimilated  in  the  third  illustration, 
are  also  phenomena,  of  character. 

)  And  if  this  conclusion  is  true,  then  is  it  not  clear  that  in- 
tellect-culture is  the  greatest  factor  in  producing  marked 
character  both  in  individuals  and  in  peoples? 

Intellect  development  (on  true  principles)  and  character 
education  are  so  related  that  they  go  forward  together ;  or,  in  I 
other  words,  that  a  weak  or  vicious  character  in  a  man   [in  / 
the  sense  in  which  these  terms  are  generally  understo(>d]  re- 
sults from  deficient  or  misdirected  intellectual  training,  and  / 
that  a  strong  or  a  virtuous  character  is  the  direct  effect  of  en-  / 
larged  intellectual  teaching  that  neglects  no  relation  man  sus- / 
tains  either  to  the  Supreme,  to  his  fellows,  or  to  the  world  of  \  / 
organic  and  inorganic  objects  that  constitutes  his  environment. ) 

The  only  intellect  to  w'hich  one  has  full  access  is  his  own, 
and  this  discussion  will  h»  better  understood  if  the  reader 
make  careful  tests  of  what  is  claimed  to  be  true  by  close  ob- 
servations on  his  own  mental  processes  in  learning. 

Observation  upon  the  workings  of  one's  own  mind  discov- 
ers that  it  forms  thought-objects  which  correspond  to  sense- 
objects,  that  thought-unities  are  created  that  represent  groups 
or  families  of  sense-objects,  and  that  thought-verities  (princi- 
ples) are  apprehended  that  represent  the  relations  of  sense- 
objects  and  groups  of  sense-objects. 


10  PEDAGOGICS. 

Furthermore,  the  observer  of  his  own  mind  will  see  that 
in  the  affairs  of  life  he  is  constantly  deciding  as  to  his  action 
in  this  or  that  by  means  of  thought-verities  acting  as  laws 
established  by  his  reason  for  the  government  of  his  conduct. 

Self-observation  will  -convince  a  candid  mind  that  the  art 
of  teaching  intellect  aright  consists  in  conducting  it  successfully 
and  consciously  through  the  three  processes,  viz :  Intellect- 
perceiving,  intellect-comparing,  and  intellect-assimilating,  and 
in  the  order  named.* 

If  truth  and  not  error  is  assinvlated,  then  the  teaching  has 
been  successful;  if  the  learner  knows  that  he  is  assimilat'mg 
new  truths  day  by  day,  then  his  teaching  has  been  conscious. 
The  pupil  whose  intellect  has  been  successfully  and  consciously 
taught  will  consciously  and  successfully — so  benign  is  the  in- 
fluence of  truth — apply  these  same  processes  in  the  affiiirs  of 
life ;  he  will  be  able  to  perceive  more  clearly,  compare  more 
correctly,  and  to  assimilate  more  advantageously  than  one  who  . 
has  been  taught  in  a  haphazard  way,  or  who  is  self-taught. 
He  will,  in  consequence,  attain  success  more  readily  (having 
fewer  things  to  learn  anew)  than  his  confreres,  the  self-taught 
and  wrong-taught. 

These  processes  utilized  by  the  educated  man  become  his 
character;  the  measure  of  character  is  power  in  utilization. 

It  follow^s,  then,  that  the  teacher  who  leads  a  pupil  success- 
fully and  consciously  along  the  pathway  of  his  development 
adds  intensity  to  his  character. 

Now  if  this  is  true,  viz:  that  intellect-education  and  char- 
acter-development are  the  same  in  kind,  i.  e. ,  that  what  develoj)s 
(intensifies)  the  one  develops  the  other,  it  follows  that  the 
problem  of  right  moral  training  is  solved  if  the  true  relations 
of  like  entities  (man  to  man,  brother  to  brother,  citizen  to 

*Itis  not  intended  to  assert  that  a  period  of  life,  say  of  years  in  (hiration, 
should  be  devoted  to  each.  The  truth  is,  that  in  a  very  short  interval  of  tinae 
the  intellect  may  act  in  each  phase  of  its  existence:  it  does  so  from  the  begin- 
ning. The  "order  named''  is  important,  because  the  completed  act,  i.  e., 
assimilation,  is  the  result  of  the  other  two.  In  the  phenomena  of  character, 
which  is  largely  the  fruitage  of  intellectual  effort,  these  same  processes  manifest 
themselves  almost  instantaneously. 


THEORY.  1 1 

citizen,  etc.,  etc.)  be  made  a  part  of  the  intellectual  equip- 
ment of  every  pupil.  This  conclusion,  which  in  effect  puts 
the  teacher  in  the  attitude  of  being  the  greatest  factor  in  the 
formation  of  moral  character,  brings  up  naturally  the  ques- 
tion of  his  responsibility.  In  determining  this,  other  data 
€nter  into  the  problem  ;  the  natural  bias  of  the  child,  the  pre- 
vious treatment  he  has  had,  and  like  considerations  varying 
in  each  case.  If  the  natural  bent  of  a  child  is  to  the  right,\ 
it  is  a  good  thing  to  make  him  strong  in  intellect  and  char-( 
acter  by  education;  if,  on  the  contrary,  his  natural  bias  is  tO| 
the  wrong,  it  would  be  hetter,  perhaps,  to  leave  him  unedu- 
cated. It  would  certainly  be  better  to  leave  him  so  if  his  evil 
tendencies  are  not  destroyed  or  greatly  modified  by  his  course 
of  training.  But  who  is  to  judge?  Clearly  it  is  no  man's 
province  to  say  who  shall  or  who  shall  not  be  educated.  It 
follows,  then,  that  society  owes  to  each  of  its  members  a 
training  adequate  to  make  him  self-sustaining;  and  in  order 
that  no  natural  thief  shall  be  endowed  with  power  to  prey 
more  successfully  upon  his  fellows,  the  further  duty  is  entailed 
of  making  general  education  moral  as  well  as  intellectual. 
This  can  be  done  only  by  putting  into  the  curriculum  those 
dements  which  are  the  foundation  for  correct  principles. 

The  conclusions  based  upon  self-observation  thus  far  drawn 
will  be  apparent  to  any  one  who  makes  a  careful  study  of  his 
own  intellect.  * 

But  are  they  true,  and  can  they  be  confirmed  by  observa- 
tions upon  actual  teaching?  The  argument  following  is  based 
upon  observations  made  in  teaching,  and  can  be  verified  by 
any  one  who  has  had  sufficient  experience  as  a  teacher. 

In  the  sphere  of  teacher  one  must  assume  that  his  pupil 
has  an  intellect  like  in  kind  to  his  own,  but  differing  in 
degree,  and  proceed  accordingly.  He  must  treat  it  also  as  a 
complex  whole.  As  is  the  body,  so  is  the  mind.  One  sees  a 
man  start  from  home  to  his  place  of  business ;  his  body 
moves,  but  at  the  same  time  his  heart  is  beating,  his  blood  is 


12 


PEDAGOGICS. 


coursing,  his  feet  are  stepping,  his  hands  are  swinging,  his 
muscles  alternately  tensing  and  relaxing,  and  his  eyes  are 
turning  here  and  there.  His  whole  physical  being,  in  fact,  is 
in  action,  each  part  contributing  to  make  up  the  grand  phe- 
nomenon called  walking.  A  very  simple  thing  is  this,  upon 
a  cursory  view,  but  a  very  complex  thing  when  it  is  analyzed. 
Such  is  the  mind  the  teacher  undertakes  to  train,  equally 
complex,  and  more  difficult  to  analyze  because  its  phenomena 
are  intangible;  and  especially  to  teachers,  because  they  are 
wont,  in  this,  as  in  all  things  (such  is  the  influence  of  our 
system  of  education),  to  take  what  some  one  says  for  the 
truth  instead  of  striving  each  for  himself,  through  observa- 
tions on  himself  and  his  pupils,  to  assimilate  the  true  laws  of 
teaching. 

To  be  the  cause  of  a  healthful,  positive  expression  of  the 
intellect  in  the  consciousness  of  the  learner,  the  teacher  must 
be  able  to  command  the  atteiition  of  that  learner  so  as  to 
cause  him  to  know  one  thought-object  from  another,  and  to 
know  numbers  of  them  ;  he  must  be  able,  by  directing  the 
memory,  to  lead  the  learner  to  perceive  the  relations  between 
his  thought-objects,  i.  e.,  their  resemblances,  their  differences, 
and  their  capabilities  for  combination;  he  must  also  be  able 
to  inspire  the  imagination  of  the  learner  to  work  out  combi- 
nations for  himself;  and  lastly,  he  must  be  able  to  direct  the 
will  of  the  learner  by  making  him  cognizant  of  the  fact  that 
what  new  combinations  he  has  made  are  a  part  of  his  mental 
structure,  and  are  to  be  used  for  his  own  good.  (What  is  for 
his  good  being  what 'is  good  for  society,  of  which  he  is  but  a 
part,  the  good  of  society  itself  at  the  same  time  being  the 
all-wise  will  of  the  Infinite.)  Truly,  a  healthful  movement 
of  the  intellect  is  a  complex  and  sublime  spectacle !  And 
verily,  he  who  brings  it  about  in  "one  of  these  little  ones" 
hath  his  reward  in  the  approving  smile  of  the  Father  of  All ! 

To  summarize  what  has  just  been  elaborated  is  to  say : 
The  mind  is  a  complex  whole,  and  must  be  treated  as  such  if 
healthfully  trained.     The  teacher  fails  in  his  aim  if  he  fails 


THEORY.  13 

to  know  that  atfentvn,  memory,  and  imagination  are  but  the 
tools  by  which  the  pupil  does  his  work,  and  that  intellect- 
culture  and  character  are  the  completed  products  of  that  w^jrk. 
He  fails  also  to  healthfully  educate  if  he  fails  to  discern  his 
true  relations  to  his  pupils.  He  can  not  give  the  pupil  the  tools, 
but  he  can  and  he  must  keep  them  sharpened;  he  can  not 
build  the  structure,  but  he  can  and  ought  to  draw  the  plan. 

There  is  in  no  case  a  healthful  action  of  the  intellect  of 
the  learner  unless  the  three  modes  of  action  defined  and 
illustrated  heretofore  exist  at  the  same  time.^ 

When  the  human  being  through  reflection  begins  to  ap- 
propriate principles  he  has  learned  as  laws  for  his  guidance 
in  the  affairs  of  life,  he  is  developing  character.  That  char- 
acter is  intensified  in  the  same  degree  as  his  power  to  apply 
his  intellect  in  the  discovery  of  truth  is  intensified.  In  other 
words,  strength  of  character  and  intellectual  power  exist  to- 
gether. Teaching  the  intellect  affects  the  character  in  degree 
in  all  cases.  But  it  can  be  made  to  affect  it  in  kind  as  well 
by  a  judicious  selection  of  thought-objects  for  the  pupil. 
And  herein  lies  the  responsibility  of  the  teacher.  He  must, 
by  a  proper  choice  of  material,  exercise  those  emotions  of  his 
pupil  that  w^ill  cause  him  to  make  a  wise  choice  in  principles 
for  his  guidance.  Now,  if  principles  are  selected  (for  the 
pupil  to  discover)  that  are  inherent  in  relations  of  himself  to 
his  fellow  pupils,  they  will  in  time  become  fixed  as  laws  with 
him,  and  he  will  have  been  educated  morally. 

It  is  to  be  observed  that  the  will  of  the  pupil  becomes  a 
factor  in  such  results;  that  it  is  a  factor  and  an  important  one 

<•"  Time  "  is  not  here  used  in  the  sense  of  moment  or  instant,  for  it  may  be 
a  much  longer  period.  Anj'  one  who  has  reflected  after  the  discovery  of  a  truth 
or  principle  will  observe  that  his  thought-objects  appear  with  a  new  force,  and 
the  thought-unities  resulting  shine  with  a  new  luster.  They  are,  in  fact,  the 
data  of  the  complete  intellectual  assimilation.  It  may  be  remarked  here  that 
the  difference  between  man  and  the  lower  animals  consists  in  this,  tnat  they 
never  abstract  a  principle  out  of  their  thought-unities,  nor  is  it  certain  that  they 
even  perceive  the  thought-verities  existing  as  relations  of  thought-objects;  re- 
flection shows  that  man  does  all  this  and  does  it  as  one  act.  And  this  is  what 
is  meant  by  the  phrase  "at  the  same  time." 


14  '  PEi^Aooaics. 

in  the  education  of  character.  It  is  a  factor  because  it  in- 
fluences the  choice  in  principles  discovered,  and  it  is  impor- 
tant because,  unless  the  pupil  is  allowed  unhampered  to  ex- 
ercise it,  his  education  is  unhealthful.  His  will  must  be 
guided,  not  broken.  But  how  is  the  will  to  be  guided  ? 
Evidently  by  exercising  the  emotions  that  are  healthful  in 
tendency.  But  how  is  this  to  be  done  ?  One  evident  answer 
is,  that  it  must  be  done  systematically ;  this  refers  to  the 
theory  that  should  govern  the  practice. 

But  there  is  another  answer  that  should  shape  the  method 
to  be  used,  and  this  answer  is  paramount.  If  this  effort  to 
improve  the  art  of  teaching  succeeds  in  doing  good,  it  will  be 
because  the  great  lesson  it  shall  convey  is,  that  the  welfare  of 
le  pupil  in  after  life  is  dependent  to  a  very  great  degree 
upon  the  method  used  in  training  him.  Method,  not  methods, 
is  the  term  used,  and  the  fact  can  not  be  too  much  empha- 
sized that  the  one  method  should  control  in  all  efforts  of  the 
teacher  in  ethics  as  well  as  in  science. 

Given  the  proper  data,  the  manner  of  proceeding  is  easily 
determined.  Now  the  proper  data  for  correct  moral  develop- 
ment are  found  in  the  happenings  of  every-day  life  at  school 
and  at  home,  in  the  history  of  individuals,  of  neighborhoods, 
and  of  nations,  and  also  in  stories. 

The  theory  and  practice  of  schools  in  the  sphere  of  moral 
training  has  inclined  too  much  to  story  telling^and  story  read- 
ing. This  is  erroneous,  for  the  reason  that  a  story  is  a  work 
of  art.  The  author  is  not  a  teacher,  and  has  not  the  sole  end 
in  view  of  engrafting  a  true  principle  upon  the  moral  nature 
of  a  responsible  human  being.  His  art  requires  certain  cli- 
maxes to  be  wrought  in  as  part  of  the  woof  of  his  story.  Re- 
wards and  punishments  are  an  invariable  accompaniment  to 
the  happy  ending  of  a  story.  For  unless  it  does  end  well  it 
will  never  go  to  press  for  a  second  edition.  This  utilitarian 
consideration  largely  shapes  the  form  of  stories. 

But  tl\ere  is  another  and  a  graver  objection  to  the  sole  use 
of  this  as  a  method.     It  is  this  :  In  stories  the  motives  of  the 


THEORY.  15 

actors  and  their  choice  of  courses  of  action  are  rarely  brought 
out  fully.  For  obvious  reasons  the  full  details  of  environ- 
ment are  never  brought  to  the  view  of  the  reader-pupil,  and 
hence  his  principles  are  only  approximately  true.  The  char- 
acter resulting  from  a  course  of  training  through  stories  will 
always  lack  in  force  and  independence,  for  the  very  apparent 
reason  that  the  pupil  in  acquiring  it  was  a  passive  imitator. 
He  is  a  fit  subject,  when  turned  free,  for  the  wiles  of  the  po- 
litical demagogue,  inasmuch  as  he  has  never  thought  for 
himself  in  assimilating  principles. 

The  objection  to  making  history  alone  the  basis  of  moral 
training  is,  that  it  is  barren  of  material  for  all  grades  of 
schools.  Tiie  great  lessons  of  policy  in  governmental  affairs 
and  in  affairs  of  like  magnitude  are  of  such  gravity  that 
they  do  not  command  the  attention  of  young  pupils.  They 
are  of  great  value  in  high-school  work,  and  their  use  with 
such  pupils  as  are  just  ready  to  struggle  with  the  problems 
of  citizenship  can  not  be  too  highly  commended.  But  things 
nearer  home,  things  within  the  world  of  the  little  ones,  are 
needed  for  primary  schools. 

Hypothetical  cases,  and  cases  of  real  happening  where  the 
names  of  the  parties  concerned  can  be  withheld,  are  the  best 
possible  material  for  this  work.  A  good  story  made  hypo- 
thetical may  be  used  for  moral  lessons.  It  is  important 
that  the  instruction  in  every  case,  whatever  the  material, 
should  be  hypothetical,  as  by  this  means  only  can  all  the 
thought- objects  and  thought-unities,  which  constitute  the  whole 
environment  of  the  thought-verity  (principle)  it  is  designed  to 
cause  the  pupil  at  that  particular  lesson  to  assimilate,  be 
brought  together. 

As  to  conduct  of  lesson  :  Principles,  as  they  shape  them- 
selves in  the  minds  of  pupils,  ought  to  be  announced  by  those 
who  conceive  them.  These  ought  to  be  taken  up  and  dis- 
cussed by  the  teacher  and  pupils.  If  erroneous,  the  miss- 
ing data  which  will  make  them  true  can  be  supplied  by  any 
one  who  has  discovered  them. 


16  PEDAGOGICS. 

Moral  lessons  conducted  in  this  way,  after  the  hypothet- 
ical method,  universal  in  scientific  investigation,  give  exercise 
to  the  will  and  leave  it  free  to  act. 

This  latter  consideration  is  of  great  importance,  because 
no  fact  is  clearer  than  that  the  will  must  be  left  unfettered  in 
order  to  the  development  of  a  character  that  will  do  right  for 
the  right's  sake.  We  all  applaud  the  immortal  sentiment 
expressed  by  Clay  in  the  utterance,  "I  would  rather  be  right 
than  President,"  and  we  despise  any  other  groundwork  as 
the  motive  for  our  actions.  The  teacher  should  prayerfully 
lead  his  pupils  to  reach  this  noble  ideal. 


POSTULATES. 


In  the  formulated  expression  of  the  postulates  and  expla- 
nations attaclud,  presented  in  this  section,  the  word  "  whole" 
is  used  to  name  all  the  thought  ohjects  contributing  to  any 
complete  intellectual  action.  These  thoiigJd-objcc's  through 
their  relations  disclose  a  truth;  they  are  in  this  sense  a 
separate  group ;   they  are  spoken  of  as  a  "  whole." 

Where  "  repetition  "  Is  enjoined  in  the  explanations  it  is 
meant  not  to  use  the  same  sense-objects  or  whatever  else 
constitutes  the  "whole"  for  that  lesson,  but  others  for  each 
repetition.  Many  repetitions  are  sometimes  necessary  to 
enable  all  membfers  of  a  class  to  grasp  a  truth. 

I.  It  is  only  through  a  "whole"  as  a  medium 
that  the  intellect  assimilates  any  truth. 

This  postulate  assumes  that  the  work  of  the  teacher  in- 
volves (1)  a  comprehension  of  the  truth  it  is  his  intention  to 
impress  at  any  given  lesson  ;  (2)  a  knowledge  of  all  the  ele- 
ments (thought-objects)  whose  relations  hold  this  truth  as  a 
content,  and  (3)  the  bringing  of  these  elements  within  the 
mental  view  of  the  pn})il. 

After  placing  the  data,  which  must  be  a  "  whole,"  before 
the  pupil,  questioning  in  the  domain  of  "what"  will  lead 
him  to  perceive  all  the  elements.  Questioning  in  the  domain 
of  ''how,"  which  includes  "  when"  and  "  where,"  will  cause 
him  to  see  differences  and  agreements.  The  question  *'  why  " 
will  lead  to  the  discovery  of  the  truth,  which  is  the  objective 
point  of  the  lesson.  For  practical  illustrations  of  the  appli- 
cation of  this  postulate  see  pages  26  and  47. 

2 


18  PEDAGOGICS. 

II.  Assimilation  of  truth  is  a  self-act,  and  is  on 
occasion. 

This  postulate  assumes  that  the  learning  of  every  truth  is 
accidental  to  the  intellect  assimilating  it.  Let  the  conditions 
exist  of  an  intellect  sufficiently  developed  to  receive  it  and  a 
"  whole"  comprehensive  enough  to  contain  it,  and  the  truth 
is  born  upon  their  conjunction.  The  teacher  is  only  one 
of  the  circumstances  that  combine  to  bring  the  proper  condi- 
tions into  existence. 

This  postulate  accounts  for  the  fact,  often  mentioned  as 
singular,  that  many  of  our  greatest  inventions  were  the  re- 
sults of  accidental  combinations. 

As  inferences  from  it  may  be  mentioned  the  following: 
The  will  of  the  learner  does  not  cause  him  to  learn  ;  neither 
can  the  will  of  the  teacher  operate  to  cause  assimilation  of 
truth ;  excessive  exertions  of  the  will  by  either  toward  this 
end  tend  to  defeat  it ;  the  will  of  the  pupil  should  be  exer- 
cised in  giving  attention,  the  will  of  the  teacher  in  building, 
repairing,  and  enlarging  the  *'  whole,"  or  in  exchanging  it  for 
another.  • 

III.  Formulating  truth  (language)  follows  the 
assimilation  of  it. 

IV.  Language  is  necessary,  and  must  become 
generic  in  order  to  any  great  intellectual 
development. 

These  two  postulates  are  important,  inasmuch  as  there  are 
many  mistakes  made  by  teachers  growing  out  of  ignorance  or 
disregard  of  what  is  assumed  in  them.  It  seems  to  be  true 
that  the  mind  is  content  to  hold  a  truth  without  language 
so  long  as  it  sees  it  in  the  relations  of  one  group  or  '*  whole." 
But  as  soon  as  it  perceives  the  same  truth  in  another  group 
a  demand  is  born  for  symbols,  as  associations,  by  which  to 
retain  the  enlarged  view  now  given  to  it.  This  demand  and 
its  application  are  illustrated  by  lessons  on  pages  27  and  41. 
That  repetition  is  necessary  in  teaching  is  an  inference  from 


POSTULATES.  19 

these  postulates.  It  is  necessary  (1)  in  order  to  create  the 
demand  for  symbols,  thereby  securing  their  retention  with 
the  proper  meanings,  and  (2)  to  fix  them  in  the  memory  with 
their  generic  meanings. 

V.   The    intellect    is    primarily  analytical,  and 
secondarily  synthetical  in  tendency. 

The  intellect  of  a  learner  looks  out  upon  nature  or  upon  a 
**  whole"  contrived  by  his  teacher,  and  all  at  first  glance  is 
chaos.  Soon  his  intellect-perceiving  enables  him  to  separate 
the  various  objects  in  view.  These  objects  in  nature  or  in 
the  artificial  grouping  are  themselves  units.  If  the  atten- 
tion is  fixed  upon  one  of  them,  the  intellect  separates  it  into 
its  parts,  and  so  on  for  the  others.  This  process  is  analysis, 
and  is  the  primary  act  of  intellect.  Transferring  the  atten- 
tion from  one  to  the  many  brings  resemblances  and  differences 
to  consciousness.  These  relations  hold  truths  as  contents 
which  are  seized  by  the  intellect.  Operating  under  con- 
ceived principles,  the  intellect  proceeds  to  make  new  units 
which  it  did  not  apprehend  at  first  glance.  This  grouping 
act  of  the  intellect,  which  seems  historically  to  follow  analy- 
sis, is  synthesis.  It  begins  with  the  first  seizure  of  a  princi- 
ple ;  it  is  that  factor  which  distinguishes  the  mind  of  man 
from  that  of  a  lower  animal ;  it  is  the  parent  of  language. 

With  this  postulate  governing  him,  a  teacher  can  so  ques- 
tion his  pupil  as  to  lead  him  far  enough  in  analysis  to  pre- 
pare him  for  certain  success  on  the  other  road.  When  syn- 
thesis has  accomplished  its  purpose  of  making  a  new  "  whole" 
for  subsequent  analysis,  the  teacher's  work  is  done  for  that 
stage  of  development. 

In  any  science  principles  taught  are  necessarily  related  to 
each  other,  and  at  every  stage  it  will  be  necessary  for  the 
teacher  to  group  facts  that  have  been  learned  as  species  out 
of  which  the  intellect  of  the  learner  shall  be  made  to  con- 
struct new  generalizations.  This  fact,  that  truths  learned  are 
species  of  higher  genera  of  truths,  makes  it  apparent  that  the 


20  PEDAGOGICS. 

human  intellect  is  capable  of  endless  development.  The  other 
fact  noted,  that  the  principles  of  a  science  are  related,  not 
detached,  suggests  with  a  force  not  to  be  questioned  that  there 
is  a  law  of  identity  in  every  science  which  contains  all  others. 

VI.  All  intellectual  processes  are  at  first  un- 
conscious. 

This  postulate  requires  the  most  delicate  management  on 
the  part  of  the  teacher,  in  order  to  prevent  doing  irreparable 
injury  to  those  pupils  who'  need  encouragement  in  their 
efforts.  The  period  of  unconsciousness  after  the  discovery  of 
a  truth  varies  in  different  individuals,  and  herein  lies  the 
danger.  The  teacher  should  exercise  the  greatest  caie  in  ob- 
serving, to  prevent  mistakes  in  judgment,  which  will  lead  him 
to  censure  where  it  is  not  deserved. 

VII.  Intellects  differ  in  degree,  not  in  kind. 

This  postulate  demands  the  same  groupings  of  "wholes" 
for  all  grades  of  intellect.  Since  repetition  is  enjoined  by 
postulates  III  and  IV,  as  essential  to  successful  teaching, 
the  opportunity  is  here  afforded  the  teacher  to  so  adapt  his 
exercises  as  to  tax  the  various  grades  of  intellect  in  the  class 
each  to  its  limit,  by  making  the  first  *'  whole"  probable  to  the 
highest  grade  only.  The  lower  grades  will  not  be  injured, 
but  be  helped  by  their  efforts  to  assimilate  through  a  *•'  whole" 
not  adapted  to  them.  A  subsequent  effort  will  more  surely 
succeed  after  the  same  truth  has  been  assimilated  through 
an  easier  "whole." 

VIII.  The  mind,  having  assimilated  a  truth  by 
intellectual  action,  has  an  innate  tendency 
to  apply  it. 

This  postulate  announces  a  fact  which  is  important  to  the 
teacher,  inasmuch  as  it  indicates  that  he  is  largely  responsi- 
ble for  the  moral  training  of  his  pupil.  Its  phenomena  are 
seen  chiefly  in  the  development  of  character. 


POSTULATES.  21 

Now,  how  can  the  teacher  bring  about  the  recall  by  the 
pupil  of  the  principle  or  law  that  should  govern  his  will  in 
any  ca?e  with  such  authority  as  will  give  it  domination  ? 

1.  The  pupil  must  assimilate  it  under  such  circumstances 
originally  as  are  parallel  to  finding  a  treasure  in  a  hollow 
tree :  no  hint  of  its  existence  must  be  given  him. 

2.  The  teacher  must  invest  the  finding  with  a  multiplic- 
ity of  associations,  in  order  to  provide  for  its  recall  in  any 
contingency  in  which  it  may  be  needed  by  the  individual. 

Take  the  principle,  "Thou  shalt  not  steal,"  for  example. 
Suppose  a  pupil's  teaching  only  covers  cases  of  taking  money, 
clothing,  watermelons,  etc.,  when  he  could  get  along  without 
them,  or  the  owner  could  well  spare  them.  Suppose,  now, 
that  individual  to  be  starving  or  naked,  or  to  have  a  hungry 
family  dependent  on  him,  and  an  opportunity  is  offered  to 
steal,  would  he  have  a  principle  that  would  dominate  his 
will?  Assuredly  not.  Can  we  not  account  for  those  cases 
of  embezzlement  and  official  stealing,  now  so  common,  by 
there  having  been  some  hypotheses  left  out  of  the  *'  whole," 
through  which  the  embezzler  assimilated  his  '*Thou  shalt  not 
steal." 

A  curriculum  of  moral  lessons  might  be  contrived,  taking 
such  abstractions  as  honesty,  friendship,  politeness,  candor, 
charity,  kindness,  etc.,  etc.,  as  its  basis.  To  teach  any  word 
so  that  it  will  go  into  the  vocabulary  is  to  follow  Postulate 
IV.  Now,  when  these  words  have  been  made  generic  by  teach- 
ing, has  the  pupil  not  also  [possibly]  been  caused  to  assim- 
ilate a  law  that  will  tend  to  dominate  his  will  when  necessary? 


PRACTICAL  LESSONS. 


The  three  primary  attributes  of  the  Intellect,  viz.,  a  Con- 
sciousness of  DiffeienC'S.  a  Consciousness  of  Agreement,  and 
Conscious  or  Unconscious  lietentiveness,  must  ever  be  kept  in 
memory  by  the  teacher  in  reading  this  section.  And  he  must 
also  bear  in  mind  the  fact  that  the  products  of  mind  action 
resulting  from  these  are:  (1)  Thought-objects;  (2)  JRchtions 
of  ThougJit-ohjects,  founded  on  Agreements  and  Differences; 
and  (3)  Tiuihs,  as  contents  of  these  relations.  And  a  third 
fact,  without  which  all  teaching  would  be  purposeless,  must 
ever  guide  him,  viz  :  A  Truth  once  existent,  the  mind  by  a 
natural  bias  tends  to  apply  it,  and  thus  becomes  self-active. 

The  eight  postulates  given,  while  originally  discovered 
and  formulated  from  observations  made  on  experiments  and 
tests  with  classes,  will  be  found  to  give  full  and  logical  ex- 
pression to  the  tacts  of  mind  noticed  above. 

It  is  not  desirable  to  separate  this  work  into  lessons,  for  it 
is  not  to  be  imitated.  The  intention  is  to  give  more  forcible 
expression  to  what  has  been  already  said,  and  to  make  clear 
that  tlie  theory  of  this  Monograph  admits  of  easy  practice. 
Yet,  if  any  one  attempts  from  one  reading  alone  to  apply 
these  postulates,  he  will  almost  surely  fail.  It  will  require 
much  study,  much  reflection,  and  repeated  trials  to  succeed. 
It  is  the  very  simplicity  of  the  whole  thing  that  will  puzzle 
the  one  who  tries  it. 

The  reader  will  find  the  word  "repetition"  often  used. 
Let  it  be  understood  that  this  system  forbids  sameness  in  rep- 
etition ;  the  same  objects  are  in  tlie  kaleidoscope,  but  as  it  is 
turned  slowly  around  there  is  endless  variety  of  beautiful  col- 
ors and  symmetrical  forms.     Kepetition  refers  alone  to  the 


PRA(rriCAL   LESSONS.  23 

truth  or  principle ;  Nature's  resources  for  the  expression 
of  the  same  j^rinciple  are  apparently  infinite ;  the  teacher 
must,  in  teaching  principles,  become  as  Nature  is,  tlie  parent 
of  variety.  The  particular  method  must  change  with  the 
number,  the  advancement  and  the  character  of  the  pupils, 
and  with  the  subject-matter.  The  esprit  de  corps  also  has 
much  to  do  with  deciding  details. 

Illustrations'  are  given  in  Arithmetic,  Language,  Geogra- 
phy, Ethic.=:,  Algebra,  and  Geometry;  but  it  is  believed  that 
a  like  application  of  the  Theory  may  be  made  in  any  and 
every  science. 

AKITHMETIC. 

Nearly  all  the  principles  of  arithmetic  are  emhraced  in 
this  outline.  Each  is  a  species  of  some  following  one,  and  a 
genus  of  some  one  that  precedes  it.  It  is  not  pretended  that 
this  series  of  principles  is  the  only  method  for  arithmetic. 
Other  species  and  genera  may  be  used.  This  is  the  best  so  far 
discovered.  Each  principle  is  to  be  taught  with  distinct 
**  wholes."  [See  Post.  I.]  With  primary  pupils  the  objects 
at  first  used  should  be  blocks,  or  similar  things,  which  in 
manipulation  remain  separated  to  the  eye.  Later,  objects 
like  straws,  which  in  part  lose  their  identity  in  handling',  and 
still  later,  cards  or  sheets  of  paper,  which  in  a  greater  degree 
are  obscured,  should  be  used.  Finally,  objects,  as  cups  of 
water,  which  entirely  disappear  as  separate  units,  ought  to  be 
used. 

In  all  the  work  the  pupil  must  be  led  to  discover  the  prin- 
ciple, the  teacher  guiding  by  proper  questions.  In  formu- 
lating the  principle  for  future  use  the  teacher  must  perfect 
the  crude  expressioti  given  to  it  by  the  pupil.  It  is  not  im- 
portant to  have  the  exact  language  used  in  this  presentation 
of  principles. 

When  the  figures  are  the  objects  usc'l,  as  in  Prin.  8^  no 
other  objects  can  be  used. 


24  PEDAGOGICS. 

PRINCIPLES. 

(1)  Totals  or  Wholes  are  the  same  when  all  their  parts 
are  the  same. 

(2)  A  whole  is  all  its  parts  put  together. 

(3)  A  whole  is  increased  by  the  increase  of  any  part. 

(4)  A  whole  is  decreased  by  the  decrease  of  any  part. 

(5)  A  whole  is  multiplied  by  multiplying  every  part. 

(6)  A  whole  is  divided  by  dividing  every  part. 

(7)  When  all  the  parts  of  any  whole  are  of  the  same  size 
or  equal,  the  part  is  a  unit,  and  the  number  of  equal  paits  is 
a  coefficient,  and  the  total  is  a  named-whole,  or  a  measured 
quantity. 

(8)  A  named-whole  is  multiplied  either  by  multiplying 
the  coefficient  or  unit. 

(9)  A  named-whole  is  divided  either  by  ;ividing  the  co- 
efficient or  unit. 

(10)  Interchanging  the  coefficient  and  the  number  of 
things  ill  the  unit  gives  same  named-whole. 

In  other  relations,  by  change  of  names,  the  coefficient  be- 
comes the  multiplier,  the  unit  becomes  the  multiplicand,  and 
the  named-whole  becomes  the  product,  and  the  8th  and  9th 
principles  become : 

(8/  Multiply  either  the  multiplier  or  multiplicand  and  the 
product  i«  multij^lied. 

(9)^  Divide  either  the  multiplier  or  multiplicand  and  the 
product  i^  divided. 

Omitting  the  objects,  the  multiplier  and  multiplicand  be- 
come factors,  and  principles  (8)^  and  (9)^  become : 

(8)5  To  multiply  either  of  two  factors  multiplies  their 
product. 

(9){  To  divide  either  of  two  factors  divides  their  product. 

Applying  10th  principle  to  (8){  and  (9)J,  and  repeating  the 
application,  gives: 

(10)^  Any  order  of  the  same  factors  gives  the  same  product. 


PRACTICAL   LESSONS.  25 

(10)"  The  prime  factors  of  the  product  of  any  number  of 
composite  factors  are  all  the  prime  factors  of  the  composite 
numbers  put  together. 

(10)"^  The  factors  of  the  H.  C.  D.  are  all  the  common 
factors. 

(10)^^  The  factors  of  the  L.  C.  M.  are  all  the  factors, 
common  and  not  common. 

(8)"  To  multiply  any  factor  multiplies  the  product. 

(9)5^  To  divide  any  factor  divides  the  product. 

(11)  The  how  much  larger  or  smaller  two  quantities  taken 
separately  are  than  a  third  quantity,  determines  the  how  much 
larger  or  smaller  one  quantity  is  than  the  other. 

(12)  The  subtraction  of  one  quantity  from  another,  and 
of  the  remainder  from  the  smaller,  repeating  till  nothing  re- 
mains, the  last  subtrahend  used  is  the  highest  unit  common 
to  both. 

If  the  condition  be  imposed  that  a  variable  product  of  two 
factors  shall  have  one  factor  constant,  (8)"  and  (9)"  give  : 

(13)  The  direct  proportion. 

If  the  condition  be  imposed  that  a  product  of  two  factors 
be  constant,  (8)"  and  (9)"  give: 

(14)  The  indirect  projiortion. 

If  conditions  be  imposed  that  a  given  number  of  things  of 
one  kind  are  to  be  put  together  in  a  whole  every  time  a  given 
number  of  things  of  another  kind  are  put  together  in  a 
whole,  then  to  find  a  new  whole  of  the  latter  kind  for  a  given 
whole  of  the  former  kind,  gives  : 

(15)  If  a  =C=  h 

then  a^  =C=  {a}  -i-  a)  x  6  or, 

(16)  If  a.  =3=  6 

then  a^  --C=  (6  -=-  a)  x  6^ 

Suggestions  follow  as  to  practice  in  teaching  these  principles. 

Prin.  1.  Except  this  principle  be  thoroughly  assimilated 

by  the  pupil,  failure  in  all  the  otiiers  is  quite  sure.     Take  a 


26  PEDAGOGICS. 

number  of  objects  (blocks  or  straws,  etc.),  without  counting, 
and  ask  the  pupil  to  make  a  pile  with  as  many  in  it,  also- 
without  counting.  Repeat  the  process  a  number  of  times. 
If  the  pupil  can  write,  let  him  try  to  write  on  his  pad  or  slate 
what  he  has  been  doing;  *  if  he  can  not  write,  let  him  state 
what  he  has  done.  When  he  thoroughly  apprehends  wliat  he 
has  done,  then  ask  him  how  the  piles  are  alike.  When  he 
has  discovered  that  they  are  alike  in  kind  and  number,  then 
ask  him  to  state  Jiow  he  knows  they  are  alike  in  number  and 
kind.  When  he  can  answer  this  question,  then  ask  iiim  to 
write  down,  with  figures,  the  name  of  the  first  pile.  To  this 
end  he  must  count  it.  When  he  has  written  the  name  of  the 
first  pile,  ask  him  to  write  the  name  of  the  second  pile.  He 
will  start  to  count  that  pile  also.  This  must  be  prevented. 
Let  him  read  over  what  he  has  discovered  as  to  the  respects 
in  which  the  piles  are  alike.  When  he  has  written  down  the 
second  })ile,  then  put  on  the  blackboard  the  results  thus : 
8  blocks  8  blocks. 
Now  ask  him  to  write  between  the  names  in  what  re- 
spects they  are  alike.  When  he  has  written,  8  blocks  are 
in  number  and  kind  like  8  blocks,  then  inform  him  that  a 
sign  is  used  to  express  the  same  thing,  and  put  on  the  board 
8  blocks  =  8  blocks,  and  ask  the  pupil  to  write  what  the 
sign  =  means.  When  he  is  able  to  write,  =  means  that  8 
blocks  are  in  kind  and  number  like  8  blocks,  he  has  made  an 
important  step.  Repetition  of  the  whole  process  must  follow 
until  he  writes,  =  means  alike  in  number  and  kind.  Then 
take  any  two  objects  of  the  same  kind,  as  two  chairs,  and 
enter  into  details  of  resemblances.  Weigh  one  chair,  or  esti- 
mate its  wei;j:ht,  and  ask  for  the  weight  of  the  other.  Take 
two  books  of  the  same  edition,  open  at  any  page,  and  ask 
pupil  to  read  what  is  in  the  other  book  at  same  place,  hand- 
ing him  the  open  book.  Do  not  be  surprised  if  he  wants  the 
other  book !  Time  sufficient  should  be  given  to  secure  a  per- 
fect assimilation  of  this  principle. 

-The  pupil  must  be  required  to  do  this  throughout  the  course. 


'     PRACTICAL   LESSONS.  27 

(2)  Let  the  pupil  make  two  wholes,  the  same  in  number 
and  kind  as  before.  Ask  him  to  separate  one  pile  into  two 
parts,  diffisrent  in  size.  Ask  him  in  what  respects  the  one 
pile  is  like  the  two  piles.  When  he  states,  "  S.ime  in  num- 
ber and  kind,"  ask  for  differences.  When  he  states,  ''  One  is 
in  two  parts,  and  in  the  other  all  are  in  one  pile,"  then  ask 
him  to  write  down  the  piles,  one  after  the  other.  Let  him 
count  every  pile.  Then  give  him  two  piles  with  different 
numbers  in  them,  and  ask  him  to  make  one  i)ile  as  large  as 
both  without  counting.  When  he  has  done  this,  ask  ques- 
tions as  before,  and  let  him  write  down  the  names  of  piles  as 
before.     On  the  board  write  results  thus  : 

5  blocks      3  blocks      8  blocks. 

Ask  the  pupil  to  put  in  signs  to  give  relations.  If  he 
can  not  use  the  signs,  then  so  conduct  the  exercises  as  to  in- 
duce him  to  write,  "  5  blocks  put  into  one  pile  with. 3  blocks 
are  the  same  in  number  and  kind  as  8  blocks,"  or  something 
equivalent,  and  then  give  the  signs,  thus: 

5  blocks  +  3  blocks  =  8  blocks. 

Repeat,  by  giving  the  pupil  three  unequal  piles,  and  ask 
him  to  make  one  pile  as  large  as  the  three  without  counting, 
and  go  through  all  the  steps  to 

7  blocks  +  3  blocks  +  2  blocks  =  12  blocks. 

Continue  in  repetition,  increasing  the  number  of  parts. 

(3)  Give  the  pupil  three  unequal  piles,  and  ask  him  to 
make  one  pile  as  large  as  the  three  without  counting.  Then 
form  three  other  piles,  each  as  large  as  the  former,  and  with 
a  whole  for  them,  all  without  counting.  Repeat  until  he  has 
as  many  sets  of  piles  as  there  are  piles  in  one  set.  Then  let 
the  pupil  form  three  equal  piles  without  counting.  Now  ask 
him  to  put  one  of  these  latter  piles  with  the  first  pile  of  the 
first  set.  Ask  him  if  the  large  pile  is  a  whole  for  the  three 
piles.  He  will  answer,  "No."  Ask  him  to  make  it  a  whole 
for  them,  and  he  will  immediately  put  one  of  the  equal  piles 


28  PEDAGOGICS. 

with  the  whole.  Repeat  this  process  with  second  and  third 
sets,  the  only  change  being  to  put  one  of  the  extra  equal  piles 
with  the  second  of  the  three  piles ;  do  likewise  with  third 
set.  Repeat  until  the  pupil  is  familiar  with  the  process,  and 
can  write  it  up.  Then,  as  the  steps  are  made  with  objects,  let 
each  be  written  up  with  figures  on  pads  or  slates,  and  then 
follow  on  the  board,  thus : 

5  blocks  +  3  blocks  -f    4  blocks  =  12  blocks.    . 

6  blocks  '         =    6  blocks. 

11  blocks  +  3  blocks  +    4  blocks  =  18  blocks. 

5  blocks  +  3  blocks  +    4  blocks  =12  blocks. 
6  ])l()cks  =    6  blocks. 

5  blocks  +  9  blocks  +    4  blocks  =  18  blocks. 

5  blocks  +  3  blocks  +    4  blocks  =  12  blocks. 
6  blocks  =    6  blocks. 

5  blocks  +  3  blocks  -f  10  blocks  =  18  blocks. 

Ask  for  and  secure  resemblances  and  differences  of  the 
three  processes  as  they  appear  on  the  board. 

(4)  Is  to  be  taught  in  a  precisely  similar  manner  to  the  3d 
principle. 

(5)  Give  the  pupil  two  unequal  piles,  and  ask  him  to 
make  one  pile  as  large  as  both.  Then  ask  him  to  make  new 
piles,  putting  two  straws  in  the  now  i)iles  for  every  one  straw  in 
thenar's;  then  to  make  a  whole  for  his  new  parts.  Then  let 
him  compare  the  number  in  the  new  whole  to  the  number  in 
the  old  whole.  He  will  answer,  "Two  for  one."  Ask  him 
how  he  knows  that  the  new  whole  has  two  straws  for  every 
one  straw  in  the  old  whole,  when  he  did  not  make  the  new 
whole  in  that  way.  If  he  can  not  answer,  repeat  until  he 
can  see  the  reason  for  the  fact.  Then,  in  repeating,  let  him 
make  two  piles  the  same  size  as  each  part  of  old  whole,  and 
put  these  equal  piles  together — another  way  to  put  two  for 
•one.     Gradually  introduce  the   expressions,  "two  piles  for 


PRACTICAL   LESSONS.  29 

one  pile/'  and  '*  two  times  one  pile,"  so  that  the  pupil  under- 
stands that  "  two  straws  for  one  straw,"  gives  same  results  as 
*'  two  piles  for  one  pile,"  and  understands  the  force  of  the  ex- 
pression '^two  times."  When  pupils  are  prepared  for  it,  let 
figures  be  used,  thus: 

4  sts.  +  3  sts.  =  7  sts.     Two  for  one  gives 
8  sts.  -f  6  sts.  =  14  sts.,  all  of  which  is  to  be  writ- 
ten from  actual  work  with  things.     Then  put,  thus : 

4  sts.  +  3  sts.  =    7  sts. 
2    =    2 

8  sts.  -f  6  sts.  =  14  sts. 

In  repetition  vary  the  number  of  parts,  and  the  number /or 
one,  until  the  pupil  is  perfectly  familiar  with  the  steps.  Like  the 
(1)  principle,  this  principle  requires  much  time  and  patience. 

(6)  To  be  taught  precisely  as  principle  (5),  except  to  take 
one  straw  in  the  new  parts  for  every  two  straws  in  the  old 
parts,  etc. 

(7)  Give  the  pupil,  say,  twelve  straws,  and  ask  him  to 
give  each  of  three  pupils  an  equal  share  without  counting. 
Give  the  pupil  any  number  of  straws,  and  a>k  him  to  separate 
them  into  a  given  number  of  equal  parts.  When  the  pupil  can 
do  this  readily,  then  let  him  form  equal  wholes,  and  ask  him 
to  separate  one  of  the  wholes  into,  say,  three  equal  parts. 
Ask  questions  ivhaty  how,  and  ichy,  as  before.  Ask  him  to- 
write  up  in  figures.  He  writes,  4  sts.  -f  4  sts.  +  4  sts.  =  12 
sts.  Give  him  three  books,  and  ask  him  to  write  that  up. 
He  will  write,  3  books.  Ask  him  to  write  up  same  number 
of  any  objects.  He  writes,  3  pencils,  3  slates,  etc.  Now  ask 
him  to  do  the  same  with  the  piles  of  straw,  and  porhnps  he 
will  write,  3  piles  of  straw.  Ask  for  name  of  pile.  He  an- 
swers, 4  sts.  Now  he  will  probably  write,  3  4  sts.  Direct 
him  to  use  the  comma,  thus  :  3, 4  sts.  Repeat  until  the  pupil 
is  famijitir  with  the  naming. 

Review  principles  (3),  (4),  (5),  and  (G)  at  this  point,, 
usincj  two  or  more  straws  in  lieu  of  one  as  a  counter. 


30  PEDAGOGICS. 

(8)  Is  taught  precisely  as  the  5th  principle,  with  perfectly- 
apparent  changes. 

(9)  To  be  taught  as  (8)  or  as  (6). 

(10)  Give  the  pupil  12  straws,  and  ask  him  to  make,  with- 
out counting,  another  whole  of  the  same  size.  Then  ask  him  to 
separate  one  of  the  wholes  into  three  equal  parts.  Then  ask 
him  to  form  new  parts,  by  taking  one  straw  from  each  of  the 
three  parts  until  all  are  gone.  Then  ask  him  to  make  a  new 
whole  for  the  new  four  equal  parts.  Ask  for  relation  of  this 
new  whole  to  the  old  whole.  When  he  answers  that  they 
are  the  same  in  number  and  kind,  ask  how  he  knows  that 
fact.  Kepeat  this  process  with  different  numbers  of  equal 
piles  until  the  pupil  assimilates  this  principle,  which  is  so 
very  important  to  much  that  follows. 

How  (8)\  (9)\  (8)},  (9)1,  etc.,  grow  out  of  the  other  prin- 
ciples from  which  they  derive  their  name,  must  be  apparent, 
on  reflection,  and  to  teach  them  is  but  a  repetition  of  the 
original  principle  with  slight  changes. 

(11)  Make  three  equal  piles  of  straws  before  the  whole 
class  without  counting  them.  Call  them  respectively  A,  B, 
and  C.  Add  two  straws  to  pile  A  and  five  straws  to  pile  C, 
and  ask  the  class  to  compare  the  number  in  A  to  the  number 
in  C.  Make  all  possible  variations  with  the  same  numbers 
in  A  and  C,  but  let  B  remain  the  same.  Let  the  pupils  write 
up  as  follows  : 

A  has  3  straws  more  than  B. 

C  has  5  straws  more  than  B. 

.-.  A  has  2  straws  less  than  C. 

A  has  3  straws  less  than  B. 

C  has  5  straws  less  than  B. 

.-.  A  has  2  straws  more  than  C,  etc.,  etc. 
It  is  well  here  to  show,  at  this  point,  the  algebraic  signs 
applicable : 

-f  3  —  (+  5)  =  —2,  first  example  above. 
—  3  —  (—  5)  =  +2,  second  example  above.* 

*  Note— This  illustration  gives  eight  cases. 


PRACTICAL   LESSONS.  31 

The  average  pupil  does  this  work  without  much  trouble. 

(12)  Is  taught  by  taking  any  two  piles  of  straws  with 
different  numbers  and  going  through  the  process  indicated. 

(13)  By  the  use  of  numbers  the  following  generic  state- 
ment is  easily  taught.  Let  A  be  the  variable  product  and  B 
the  variable  factor  and  C  the  constant  factor;  then  multiply- 

A  =  BC 
Ai=  B^C 


ing  or  dividing  B  multipb'es  or  divides  A, 
whence  A  -^  A^  =  B  -f-  B^  whence  A  :  A^ 
=  B  :  B\  the  direct  proportion. 
(14)  By  the  use  of  numbers  the  following   is   likewise 
easily  taught.     Let  A  be  the  constant  product  and  B  and  C 


A=  BC 
A  =  Bi-  C 


the  variable   factors ;    then,  multiplying   B 
divides  C,  whence  B  -h  B^  =  C^  ~-  C,  or 
B  :  B^  =  C^  :  C,  the  indirect  proportion. 
(15)  (16)  Are  so  easily  taught  by  the  use  of  straws  and 
blocks  that  illustration  is  not  needed. 

HOW  TO  USE  EXAMPLES  FROM  TEXT-BOOKS. 

Alternating  with  and  supplementing  the  work  already 
given,  much  practice  by  the  pupil  must  be  had  in  working 
problems.  These  may  be  originated  by  the  teacher,  or  taken 
from  books.  In  every  case  they  should  be  made  to  serve  as 
additional  *'  wholes"  to  secure  assimilation  of  principles. 

It  is  thought  to  be  necessary  here,  before  leaving  the  sub- 
ject, to  enter  into  details  somewhat  as  to  how  to  use  the  ex- 
amples so  as  to  secure  the  end  desired,  i.  e.,  to  make  them 
repetitions.  It  is  to  be  noted  that  examples  from  books  have 
not  been  recommended  till  after  the  principle  has  been  assim- 
ilated through  objective  teaching.  This  recommendation, 
therefore,  presumes  the  existence  of  the  principle  in  the  mind 
of  the  pupil,  although  in  an  inchoate  state.  The  first  ques- 
tion when  an  example  is  presented  should  be,  "  What  princi- 
ple is  contained  here?"  A  failure  to  get  the  proper  answer 
need  not  discourage  the  teacher,  as  it  is  for  some  time  the  rule 
and  not  the  exception. 


32  PEDAGOGICS. 

Questioning  in  the  domain  of  *'  what,"  "  how,"  and  "  why," 
will  lead  to  its  discovery  and  to  the  proper  solution.  With 
large  classes  it  is  well  to  have  all  do  simultaneously  on  pads 
or  slates  what  the  teacher  does  on  the  board  in  response  to 
answers  to  his  questions. 

In  general,  a  number  of  problems  can  be  treated  in  a  les- 
son. After  tliis  study  of  a  lesson,  the  whole  work  should  be 
erased,  and  the  pupils  required  to  make  an  exact  reproduction 
of  it  for  the  next  time.  This  reproduction  lesson  is  a  valu- 
able one,  as  it  leads  the  way  to  independent  work  by  steps 
possible  of  accomplishment  by  all. 

More  difficult  practice  is  secured  by  leaving  all  numbers 
blank  in  the  example  under  consideration,  proceeding  by 
questions  as  before.  Examples  treated  in  this  way  may 
be  left  on  pads,  the  requirement  for  the  reproduction  lesson 
being  to  fill  the  blanks,  and  bring  solutions  according  to  usual 
forms  of  written  answers. 

When  the  details  of  operations  (addition,  multiplication, 
etc.,)  have  become  automatic  through  practice,  and  mistakes 
are  ho  longer  made,  it  is  advisable  to  have  solutions  formu- 
lated by  signs,  to  express  the  operations  necessary. 

Note— If  a  teacher  instructs  after  this  method  throughout  the  whole  course 
in  numbers,  the  tables  will  be  learned  incidentally,  just  as  the  letters  are 
learned  through  the  application  of  the  word  method  in  teaching  reading. 


LANGUAGE. 

The  illustrations  in  language-work  to  follow  will  be  em- 
braced under  the  following  headings :  Word  Teaching,  Reading, 
and  Grammar. 

Introductory  remarks  are  inserted  here  to  elucidate  the 
relations  of  the  postulates  to  such  work. 

The  necessity  for  language  is  felt  by  an  individual  who 
wishes  to  impart  his  thoughts  to  others  or  to  liimself;  its  con- 
venience is  felt  by  one  who  wishes  to  recall  a  principle  in 
order  to  apply  it,  or  a  thought-object  in  order  to  compare  it 


PKACTICAL   LESSONS.  33 

with  others.  It  is  pertinent  to  remark  here  that  memorized 
definitions  fail  to  serve  the  convenience  of  the  learner.  His 
own  formulations  only  are  availahle  to  him  for  progress  in  in- 
tellectual work.  Constant  opportunities  ought,  therefore,  to 
be  given  him  to  write  his  own  definitions,  rules,  or  other  prin- 
ciples assimilated. 

What  was  said  in  regard  to  the  necessity  of  language  is  of 
such  importance  to  progress  in  its  use  that  it  is  almost  worthy 
of  being  formulated  as  a  separate  postulate.  Its  bearing  upon 
teaching  will  be  apparent  when  one  reflects  that  unless  the 
pupil  has  the  motive  to  impart  his  knowledge  at  the  time  he 
gets  it,  then  no  necessity  can, exist  for  its  use,  and  he  will  lapse 
into  inattention  during  the  lesson,  or  forget  the  fact  after- 
ward. 

If  the  pupil  is  made  conscious  of  what  he  learns  [see  page 
10]  the  desired  end  will  be  reached,  for  he  has  the  giving  mo- 
tive as  an  inheritance. 

Thought-objects  record  themselves  in  language  as  words, 
phrases,  clauses,  and  sentences;  thought-unities  take  form  as 
generic  words  and  sentences,  and  thought-verities  as  sentences, 
either  elliptical  or  complete. 

When  a  tangible  object  has  been  perceived,  and  its  asso- 
ciations with  the  individual  perceiving  are  intimate,  a  necessity 
exists  for  a  name  for  it.  Proper  names,  as  Fido  and  William, 
are  the  only  formulations  from  intellect-perceiving. 

When  the  second  step,  comparing,  has  been  made  by  the 
intellect,  class  names,  as,  horse,  running,  swiftly,  black,  etc.,  are 
learned.  Phrases  expressive  of  relations,  as,  with  a  stick,  on 
a  fence,  in  a  field,  are  also  conceived.  Complex  relations,  as, 
The  black  horse  7'uns  in  afield,  The  tree  is  bending  before  the  wind, 
are  likewise  apprehended  at  this  stage. 

When  the  intellect  has  completely  acted  in  any  case,  a 
general  truth  or  a  universal  truth  has  been  assimilated.  It 
exists  as  a  content  of  certain  relations  of  certain  thought- 
objects  that  have  been  brought  together  as  a  **  whole."  Ex- 
amples of  such  mind-action  formulated  are.  The  vnnd has  force. 
Sustenance  is  necessary  to  life.         3 


34  PEDAGOGICS. 

This  analysis  of  the  fuuctions  of  language  is  thought  to  be 
necessary  for  the  teacher  to  enable  him  to  intelligently  direct 
those  under  his  charge.  The  following  principles  are  recom- 
mended to  teachers,  to  be  used  in  the  manner  outlined  below, 
in  connection  with  both  reading  and  grammar  lessons.  They 
will  serve  the  purpose  of  "  waking  up"  the  pupil  to  a  com- 
prehension of  what  he  does  in  talking,  writing,  reading,  and 
hearing.  Frequent  repetitions  are  necessary  to  insure  assim- 
ilation. 

I.  Sentences  are  identical  when  all  their  words 

are  identical. 

II.  Sentences  vary  in  meaning  as  their  words 

vary. 

III.  A  sentence  has  essential  parts  which,  put 
together,  make  up  the  meaning. 

IV.  Each  modifier  of  the  predicate  decreases  its 
horizon  of  meaning.  [The  subject  is  regarded  as 
a  modifier.] 

The  following  method  of  presenting  the  data  for  these 
principles,  it  is  believed,  will  recommend  itself  for  its  sim- 
plicity and  directness. 

PKINCIPLE   I. 

Write  two  or  three  sentence^ exactly  identical  as  far  as  the 
words  that  compose  them  are  concerned,  as  : 
Mary  loves  her  doll. 
Mary  loves  her  doll. 
Alary  loves  her  doll. 

Ask  the  following  questions  :* 

Are  these  expressions  alike  in  meaning? 

There  are  very  few  who  will  not  unreservedly  answer, 
*'Yes,"  to  this  question.  If  ''yes"  is  the  general  answer, 
continue  questioning  in  "what"  after  this  manner,  "How 
many  parts  (words)  in  each?"     "What  does  Mary  mean?" 

'■'It  is  better  to  have  answers  written,  as  sueli  a  course  secures  effort  on  the 
part  of  each  pupil. 


PRACTICAL   LESSONS.  35 

"loves?"  "her?"  "doll?"  Does  Mary  mean  the  same  in 
each  sentence?  Division  in  opinion  inevitably  resnlts  at  this 
point  if  the  teacher  has  held  the  attention  Avell. 

Continue  by  questioning  with  "  haw."     For  example: 
How  do  you  know  the  Mary  is  the  same  in  each  sentence? 
Is  there  only  one  Mary  in  the  world  ?    All  will  agree  that  if 
different  Marys  are  meant  different  meanings  attach  to  the 
sentences. 

Question  further :  "  If  the  Marys  are  different,  can  the 
dolls  be  the  same?"  Agreement  will  again  result  in  saying 
that  the  dolls  are  different.  The  class  that  is  thus  led  to  agree 
will  also  agree  in  saying  that  "  Sentences  are  identical  when 
their  words  or  parts  are  the  same  in  meaning,"  if  the  question 
is  asked.  A  complete  assimilation  can  be  secured  by  an- 
nouncing that  the  sentences  are  indentical  in  meaning,  and 
then  asking  "  why?" 

PRINCIPLE   II. 

Make  changes  as  follows  : 

1.  Mary  loves  her  doll. 

2.  Mary  loves  her  cat. 

3.  Mary  loves  her  mother. 

4.  3Iary  loves  her  hreakjast. 

Call  for  resemblances  and  differences  in  the  separate  units 
(sentences).  Question  in  the  domain  of  "  what"  until  all  the 
meanings  in  "loves"  are  brought  to  view  according  to  its 
modifiers,  doll,  cat,  mother,  breakfast.  There  are  also  different 
meanings  to  "  her"  in  the  separate  sentences  which  might  be 
brought  to  view  by  questioning,  but  it  will  not  be  necessary 
to  be  exhaustive  in  analyzing  the  units  into  their  parts.  Com- 
pare (1)  and  (2)  by  questioning  as  to  how  the  separate  mean- 
ings result.  If  necessary,  change  "  cat"  to  "  doll "  in  (2),  in 
order  to  make  them  identical.  Compare  others  in  the  same 
way,  keeping  the  intellect  busy  in  observing  "how"  differ- 
ences result. 


36  PEDAGOGICS. 

Add  other  sentences  to  the  group,  such  as  : 

5.  3fary  loves  my  doll. 

6.  3Tary  loves  everybody. 

7.  3Iary  loves  a  hot  breakfast. 

Make  the  comparison  of  the  new  sentence  with  another  in 
the  group  from  which  it  differs  in  only  one  word,  and  the  an- 
swer to  "  how"  will  take  the  form  :  By  changing  the  "  her" 
in  (1)  to  "  my"  in  (5).  By  changing  "  her  mother  "  in  (3) 
to  "  everybody"  in  (6),  etc.,  etc.  When  the  class  have  _per- 
ceived  and  compared  consciously  in  answer  to  "what"  and 
*'  how,"  they  will  readily  assimilate  the  principle  in  answer  to 
the  question,  "  Why  do  sentences  vary  in  meaning?" 

PRINCIPLE   III. 

Arrange  the  words  of  a  short  story  in  columns,  thus : 

air  the  Henry 

John  threw  a 

large  other  in 

it  caught  ball 

persons  into  William 

every  and  his 

hands  play  saw 

enjoyed  them  '     several 

their  one  at 

much  very  it 

Tell  the  class  that  these  are  the  words  of  a  story.  Ask 
them  to  look  over  the  list  and  tell  what  things  happened. 
The  result  will  no  doubt  be,  seeing,  throwing,  catching,  lAayiiig, 
enjoying. 

Ask  who  did  these  things,  and  get,  William,  John,  Henry^ 
persons. 

Ask  when  these  things  happened ;  the  past  form  of  the 
verbs  will  give  a  cue  in  this  case. 

Ask  in  what  order  the  happenings  took  place.     This  will 


PRACTICAL   LESSONS.  37 

result  in  getting  throwing,  catching,  seeing,  and  enjoying,  as  the 
natural  order  of  events. 

After  arranging  who  did  the  throwing,  etc.,  the  class  are 
prepared  to  write  the  story,  as  follows : 

*'  William  threw  a  large  ball  into  the  air.  Henry  caught 
it  in  his  hands.  John  and  several  other  persons  saw  them  at 
play.     Every  one  enjoyed  it  very  much." 

On  the  first  trial  many  of  the  minor  modifiers  will  be 
overlooked.  They  can  be  supplied  by  asking  questions  like 
the  following:  What  is  large  used  for?  Into  what,  do  you 
suppose?     At  what?     Enjoyed  vilvAi'l  etc.,  etc. 

When  the  complete  story  has  been  constructed,  question 
upon  the  office  of  the  several  words  used.  This  is  but  going 
over  tlie  same  ground  again,  and  it  will  be  found  that  the 
pupils  will  answer  promptly,  as  follows: 

To  tdl  what  happened,  to  tell  who  did  something,  to  tell  where 
it  ivas  thrown,  etc. 

Lead  them  tlien  to  observe  that  each  sentence  has  (1)  a 
word  to  tell  what  is  said,  (2)  a  word  to  tell  what  it  is  said  of, 
and  (3)  phrases  or  words  to  tell  kind,  time,  manner,  -place,  etc. 

Call  these  predicate,  subject,  and  viodifiers,  and  have  them 
point  them  out  in  other  sentences.  Several  repetitions  of  this 
work,  or  something  similar,  will  be  necessary  to  secure  com- 
plete assimilation  of  the  principle. 

PRINCIPLE   IV. 

Commence  with  part  of  a  phrase,  thus : 

Into  tJie, 

and  have  the  members  of  the  class  to  suggest  endings,  as 
follows : 

fair 

I  water 
1.  Into  the  -{  room 

I  house 

t  etc. 


38 


PEDAGOGICS. 


Combine  into  the  generic  phrase,  into  something  or  some- 
ivhere.     Selecting  one  of  the  species,  continue  thus: 

(  arrow 
1  ball 
2.   Into  the  air  the^  bird 
I  stone 
tetc. 

Proceeding  as  before,  construct : 

f  sped 

I  flew 

3.  Into  the  air  the  arrow  •{  shot 

I  went 
l^  etc. 

Selecting  again,  complete  the  sentence  : 

4.  Into  the  air  the  arrow  sped. 

Compare  (1),  (2),  (3),  and  (4),  with  a  view  of  making 
the  assimilation  that  sped  fixes  the  meaning  of  the  whole. 

Taking  sped  as  the  basis,  construct  the  equivalent  general- 
ization : 

Something  somewhere  sped. 

Construct  a  horizon  to  represent  this  meaning,  and  smaller 
ones  within  it  to  represent  the  restricted  meaning  as  modifiers 
are  added,  thus: 


PRACTICAL   LESSONS.  39 

Numbering  the  horizons  as  in  the  diagram,  and  setting  up 
a  comparison  among  them,  the  pupil  may  be  led  to  make  the 
assimilation  formulated  by  the  principle. 

Many  repetitions,  however,  will  be  necessary  in  order  to 
secure  thorough  mastery  of  it. 

Note.— A  complete  generic  idea  involving  every  element  may  be  expressed 
by  the  following  formula: 

Something,  somewhere,  sometime,  somehoiv,  somewhy,  -1  ^^1'^ 

The  predicate  or  verb  in  assuming  tense  form  expresses  always  existence,  or 
its  alternative  action,  and  generic  time,  and  holds  elliptically  the  other  elements 
of  the  idea.  All  modifiers  of  the  predicate  are  but  expressions  of  the  character 
of  certain  elements  in  the  idea  seeking  expression.  If  any  particular  element 
only  demands  a  generic  expression  it  does  not  assume  form ;  if  it  exists  in  a 
specific  degree  some  adjunct  or  word  as  a  modifier  of  the  elliptical  form  ex- 
presses it. 

The  modality  of  the  idea  is  expressed  by  the  particular  form  its  language 
representative  takes,  viz.,  as  a  statement,  as  an  interrogatory,  or  as  a  command. 

The  quantity  of  the  idea  is  expressed  by  the  modifiers  as  a  group  or  whole. 

Illustrations  are  given  below. 

I.  1.  Something:  A  night  of  storm. 

2.  Somewhere:  (held  generically.) 

3.  Sometime:  (expressed  in /o?/oi<;gd.) 

4.  Somehow:  (expressed  ii\  followed.) 

5.  Somewhij :  (held  generically.) 

6.  {  f  2.f-"* "  }  ^o^lowed  a  day  of  sunshine. 

7.  Its  modality  is  apparent  in  the  fact  that  it  is  a  statement. 

8.  Compare : 

A  night  of  storm  follows  a  day  of  sunshine, 

^Mghts  of  storm  (jj'jfj^}  followed  by  {jJalj^^}  o^  f^unshine,  or  other  ex- 
pressions of  similar  ideas  to  that  under  analysis,  and  the  qnantity  becomes 
apparent. 

II.  1.  Something:  my  father. 
6.  Exists;  sometime:  lived. 

2.  Somewhere:  beside  the  Tyne. 

The  other  constructive  elements  are  held  generically  in  "lived,"  and  are 
therefore  elliptical.  The  modality  and  quantity  will  be  apparent  through  com- 
parison. 

"^'    timetime:}  dawn  and  lend  (thine  aid). 

A    <inmi>hr,n,  ■  i  o"  our  darkucss  (modifies  generic  idea  in  "  dawn  ")• 
4.  i>omeiiow.   -^  U5  _  (^^  ^g)  (modifies  generic  idea  in  "  lend  "). 

"  Thine  aid  "  is  a  modifier  of  the  elliptical  object  inhering  in  "  lend."  The 
other  constructive  elements  are  h<4d  generically  in  the  predicate,  and  modality 
and  quantity  are  apparent  iu  the  form. 

Other  examples  are  not  necessary  to  make  apparent  the  fact  that  every  Eng- 
lish sentence,  whatever  its  mode,  may  be  analyzed  as  the  examples  are  by  com- 
"paring  with  the  generic  sentence. 

Reflection  will  show  that  if  sentences  are  studied  as  "wholes"  in  this  way, 
and  comparisons  made  in  the  manner  indicated,  that  the  assimilations  made  by 
the  pupils  will  be  of  the  highest  value  to  them  in  understanding  what  they 
read,  and  in  expressing  their  thoughts  with  clearness  and  force. 


40  PEDAGOGICS. 


WORD    TEACHING 


When  a  child  first  enters  school  he  has  a  large  stock  of 
words  in  his  speaking  vocabulary.  The  aim  of  the  teacher 
should  be,  at  this  stage  of  his  education,  to  make  him  ac- 
quainted with  iJiPse  in  their  written  and  printed  forms. 

This  is  the  primary  course  of  study  in  reading.  By  neces- 
sity some  new  words  will  be  added  to  his  vocabulary  during 
the  two  or  three  years  necessary  to  bring  him  up  with  what 
he  already  knows. 

If  this  is  well  done,  his  after  work  in  reading  is  easy. 
But  at  every  stage  of  his  education  his  teacher  ought  to 
present  thoroughly  all  the  new  word  material  he  encounters 
in  his  text-books. 

An  illustration  is  given  below  of  how^  this  should  be  done, 
both  witli  w^ords  already  in  the  vocabulary  and  with  words  it 
is  desired  to  put  there. 

In  this  work  the  teacher  should  have  Postulates  III  and 
IV  in  mind.  The  illustrations  are  taken  from  actual  practice, 
the  first  with  a  class  during  their  second  month  in  school, 
the  second  with  children  entering  upon  their  third  year. 

Teacher  (writing  the  word  "run"  on  a  card):  Who  can 
tell  me  what  that  says  ? 

Pupil  (selected  from  a  number  who  volunteered)  :  It  says 
run. 

T. :  Can  you  run  ? 

The  pupil  assented,  and  after  a  little  persuasion  ran  to  his 
seat.  The  teacher  then,  to  test  their  knowledge  of  the  word, 
asked  questions  and  got  the  following  statements : 

A  boy  can  run. 

A  horse  can  run. 

Inquiring  as  to  the  difference  in  the  running,  he  found 
they  associated  it  with  the  legs.  This  indicated  that  the 
meaning  was  not  generic  to  them.  The  next  question  was, 
**Can  a  box  run?"  This  produced  a  general  laugh,  and 
many  emphatic  "noes."     ''Why  not?"  asked  the  teacher  of 


PRACTICAI.    LESSONS.  41 

one  pupil,  who  evidently  had  a  reason  in  his  mind.  "  Because 
it  has  no  legs,"  was  the  prompt  reply. 

"  Can  a  wao^on  run  ?  "  asked  the  teacher.  There  was  some 
hesitation,  but  many  answered,  "  Yes."  "  But  it  has  no  legs; 
how  is  that  ?"  There  was  quiet  for  some  time.  At  length  a 
hand  went  up,  and  the  very  wise  reply,  ''Its  wheels  are  its 
legs,"  was  mo'lestly  given.  The  teacher  then  illustrated  the 
meaning  of  the  word  by  calling  attention  to  the  clock  which 
was  ruanwg  and  to  water  on  a  sheet  of  paper,  anr]  left  the 
word  for  another. 

The  perceivinri  powers  of  the  children  had  been  exercised 
in  recognizing  the  different  actions ;  their  compirinrj  powers 
had  been  exercised  in  observing  the  differences  and  resem- 
blances in  the  actions.  Their  asiimilatlng  powers  were  prob- 
ably exercised  in  getting  a  more  generic  meaning  for  the 
word.  This  latter  was  the  aim  of  the  teacher;  how  well  he 
succeeded  could  only  be  known  by  testing  the  class  at  some 
subsequent  les-on. 

Tiie  next  illustration  is  of  a  new  word.  A  girl  had  asked 
to  have  the  word  "fiitigued"  from  the  reading  lesson  ex- 
plained. The  teacher  persuaded  her  to  run  to  and  fro  in  the 
room  a  number  of  times.  After  she  had  done  this  she  was 
asked  how  she  felt.  "I  feel  tired,"  Wi\^  the  reply.  ''Some 
people  would  say  fatigued  "  remarked  the  teacher. 

Both  words  were  then  written  on  the  board  and  copied  by 
the  children.  A  comparison  was  set  up  by  suppositions  as 
follows:  How  are  you  apt  to  feel  if  you  sit  awhile  after  you 
are  tired  or  fatigued  ?  Does  your  teacher  feel  fdgued  or 
tired  after  her  day's  work  ?  Have  you  ever  had  a  tired  feel- 
ing after  school  or  after  studying  a  long  while?  Did  you 
ever  hear  any  one  say  she  was  exhausted^  [This  word  was 
added  to  the  group  on  the  board  and  copied  when  a  child 
answered  affirmatively.]  What  had  she  done  to  exhaust 
her?  Was  Mary  exhausted  awhile  ago?  When  would  you 
use  exhausted^  When  would  you  use  tired f  When  use 
fatigued  f 


42  PEDAGOGICS. 

The  answers  of  the  children  are  not  given,  nor  the  whole 
conversation.  The  children  were  led  to  observe  that  fatigued 
is  a  species  of  tired,  and  that  exhausted  is  tired  carried  so  far 
that  a  person  has  to  stop.  This  was  illustrated  by  the  prim- 
itive meaning  of  the  word. 

It  was  not  possible  nor  desirable  at  that  lesson  to  make 
the  meaning  fatigued  generic.  The  aim  of  the  teacher  was 
simply  to  have  the  class  perceive,  compare,  and  classify  it. 
That  this  was  probably  done  will  be  apparent  to  one  who 
scrutinizes  the  work. 

No  formal  statement  was  attempted  of  the  truths  taught 
in  either  lesson,  nor  was  a  definition  essayed  for  any  word. 
All  proper  word  teaching  contemplates  a  trial  at  the  it.se  of 
the  word  at  some  later  period.  This  serves  both  as  a  review 
and  a  test  of  the  work  done. 

READING. 

In  the  primary  course  the  pupil  deals,  as  a  rule,  with  words 
he  already  knows  the  mt-aning  of. 

At  the  time  he  learns  to  know  the  written  or  printed  form 
his  teacher  ought  to  make  the  effort  to  have  him  assimilate  a 
more  generic  meaning  for  each  word.  In  addition  to  his  les- 
sons in  learning  words,  which  is  the  foundation  for  pn^gress, 
he  should  also  have  lessons  in  learning  phrases,  such  as,  on  a 
box,  into  a  house,  to  the  wall. 

There  are  many  prepositions  and  other  such  words  whose 
meanings  are  not  susceptible  of  objective  illustration  or  of 
clear  definition.  If  phrases  are  taught  in  the  same  way  as 
words  are,  these  meanings  are  assimilated. 

The  main  difficulty  in  teaching  reading  has  always  been  to 
get  the  children  to  comprehend  the  meaning  of  the  sentences 
before  them.  This  difficulty  will  always  exist  to  the  teacher 
who  requiies  a  child  to  learn  to  read  by  reading  another  per- 
son's thoughts.  If  the  hist  year's  work  in  reading  were  to 
be  entirely  of  sentences  of  his  own  composition,  it  is  believed 
that  the  load  would  be  lifted  in  a  great  measure.     Observa- 


FKACTICAL    LESSONS.  43 

tion  will  convince  anyone  that  the  more  nearly  a  teacher  con- 
forms to  this  rule,  the  more  easily  do  his  pupils  learn  to  rea«l. 

To  express  this  principle  in  practical  form  would  be  to  say: 
A  child  will  learn  to  read  more  readily  if  he  makes  the  first 
series  of  lessons  for  himself. 

In  reality  he  does  this,  if  he  learns  at  all,  for  it  is  mani- 
festly impossible  for  one  to  get  the  author's  exact  thought  in 
any  case. 

The  product  from  reading  a  sentence  to  any  mind  is  not 
the  thought  of  the  author,  but  the  thought  of  the  reader 
coming  into  the  mind  as  an  assimilation,  from  the  relation  of 
certain  thought-objects,  suggested  by  the  words  of  the  sen- 
tence, standing  before  him  as  "  whole." 

Unless  a  child  has  had  practice  in  expressing  relations  ob- 
served, he  is  not  prepared  to  analyze  such  relations  when  ex- 
pressed by  another.  The  oral  expression  of  relations  does  not 
resemble  the  equivalent  written  or  printed  relation  to  a  great 
enough  degree  for  the  pupil  to  recognize  their  idenity  until 
he  has  made  the  intermediate  step  of  formulating  some  of  the 
relations  he  has  observed. 

To  illustrate  all  this :  Suppose  the  mind  holds  as  a  complex 
picture  the  following  thought-objects :  A  dog — aboy — chasing — 
a  road — across  (something)  —and  past  time.  It  is  easy  for  that 
mind  to  compose  the  whole  into  one  complex  relation,  and 
say :   "  The  dog  chased  the  boy  across  the  road." 

After  doing  this,  and  recognizing  the  written  words,  "  the 
dog  chased,"  etc.,  as  being  identical  with  the  same  words 
spoken,  he  can  easily,  on  hearing  or  seeing  something  written 
in  the  same  idiom,  get  a  thought  from  it.  The  fact  that 
children  are  unwittingly  put  to  work  in  strange  idioms,  when 
set  to  practice  in  first  readers  and  primers  prepared  by  dis- 
tinguished (?)  authors,  accounts  for  much  of  the  labor  ex- 
pended by  primary  teachers. 

Nothing  is  easier  than  to  get  children  themselves  to  make 
the  first  lessons  they  are  to  read. 

A  description  of  the  teacher's  desk  and  the  objects  upon 


44  PEDAGOGICS. 

or  near  it,  with  their  relations  to  each  other  and  to  the  desk  ;  a 
narrative  of  the  adventures  they  had  when  it  rained,  and  they 
could  not  go  out  to  recess;  a  description  of  a  doll  party  in 
progress  before  them;  a  description  of  see-sawing,  or  some 
other  game ;  in  fact,  all  the  events  and  scenes  of  home  or 
school  life  are  open  to  the  teacher  for  selection. 

But  care  must  be  taken  to  have  the  lessons  as  recorded  for 
practice  expressed  in  their  own  idioms.  They  must  be  led  by 
degrees  to  express  themselves  in  the  forms  used  by  older  peo- 
ple. As  a  rule  they  can  not  get  thought  from  sentences  pre- 
pared by  mature  minds  until  they  have  adopted  to  some 
extent,  in  conversation,  the  habitual  forms  of  expression  be- 
longing to  maturity. 

The  principles  thus  far  illustrated  as  applicable  to  primary 
work  in  teaching  reading  apply,  with  modifications,  through- 
out the  course. 

1.  New  word-material  must  be  introduced  objectively,  and 
at  subsequent  lessons  the  specific  meanings  assimilated  must 
be  made  generic. 

2.  Lessons  upon  phrases  and  clauses  and  sentences  must 
be  given,  alternating  with  the  practice  lessons.  Repetitions 
of  such  work  as  has  been  recommended  under  Language 
serves  the  purpose  indicated. 

3.  Reproduction  of  lessons  read,  or  abstracts  prepared  in 
advance  of  lessons  that  are  very  difficult,  are  valuable  as  read- 
ings for  classes. 

An  outline  of  the  work  contemplated  by  (3)  is  given  below. 
The  lesson  selected  for  outline  is  taken  from  Butler's  Fourth 
Reader.  Have  the  children  dictate  the  following,  from  in- 
spection of  the  lesson  if  new,  from  memory  if  they  have  al- 
ready recited  it : 

CHARACTERS, 

a  Brahmin,  a  third  rogue, 

a  rogue,  a  dog, 

a  second  rogue,  the  gods. 


PRACTICAL   LESSONS.  45 

HAPPENINGS.  TIMES. 

vowing,  a  certain  day, 

going  to  buy,  at  same  time, 

inventing,  before, 

questioning,  just  then, 

replying,  soon  after, 

exclaiming,  later, 
protesting, 

paying,  places. 

sacrificing,  the  market  place, 

smiling.  home  of  Brahmin. 

Other  groups,  as  motives,  to  cheat,  to  sacrifice,  etc.;  or  re- 
lated THINGS,  as  bag,  pot  of  ghee,  etc.,  etc.,  may  be  added 
if  necessary  to  comprehension  of  the  "  whole." 

Enough  questioning  must  be  done  in  what  and  how  to  enable 
the  children  to  get  a  firm  mental  grasp  of  the  story. 

Let  them  write  it  in  character,  that  is,  let  one  tell  it  from 
the  standpoint  of  the  author,  another  as  the  Brahmin,  another 
as  one  of  the  rogues,  and  still  another  as  the  dog,  or  one  of 
the  gods. 

Select  meritorious  efforts  as  matter  for  reading  lessons. 
These  ought  to  be  copied  on  separate  sheets  for  preservation. 

GRAMMAR. 

To  present  this  subject  successfully,  the  teacher  must  lead 
the  pupil  to  assimilate  the  principles  underlying  constructions 
through  his  own  experiences.  In  other  words,  the  pupil's 
own  sentences,  or  sentences  made  b^''  the  teacher  using  only 
words  that  are  in  the  pupil's  vocabulary,  must  be  the  basis  for 
comparison. 

In  general,  any  principle  of  grammar  may  be  taught  by 
composing  a  group  of  sentences  or  phrases  having  the  prin- 
ciple desired  to  be  taught  prominent,  either  as  a  resemblance 
or  as  a  difference. 


46  PEDAGOGICS. 

For  example,  suppose  it  is  desired  to  prepare  the  pupil 
to  understand  the  definition,  "A  noun  is  in  the  nominative 
case  when  it  is  the  subject  of  a  verb."  Compose  a  group 
similar  to  the  following : 

1.  A  boy  walks. 

2.  A  horse  walks. 

3.  A  man  walks. 

4.  A  cow  walks. 

Question  upon  the  details  of  meaning  in  these  sentences 
and  in  the  particular  words  until  the  pupil  loses  sight  of  the 
words  that  compose  them.  He  will  do  this  when  you  enable 
him  to  picture  in  his  mind  the  different  acts.  His  percep- 
tion must  be  made  clear.  Proceed  by  comparing  to  discover 
that  boy,  horse,  man,  and  cow  have  a  common  use,  viz.,  to  tell 
which  animal  walks. 

Add  others  to  the  group,  varying  as  below  : 

5.  A  toad  hops. 

6.  A  squirrel  leaps. 

7.  A  bird  flies. 

By  comparing  these  with  the  others,  the  resemblance, 
which  still  holds  throughout,  will  assume  a  more  generic 
form,  thus :  To  tell  which  animal  moves. 

In  the  same  way  "which animal"  may  be  made  to  assume 
the  form,  "which  thing,"  and  "moves"  to  take  the  more 
generic  meaning,  "  acts." 

This  case  or  use  of  a  noun  needs  a  name,  and  after  giving 
it,  the  pupil's  crude  answer  to  the  question,  "  When  is  a  noun 
used  in  the  nominative  case?"  compared  Avith  the  definition 
given  in  the  text-book,  will  enable  him  to  comprehend  the 
latter. 

The  same  word,  used  in  different  ways  in  a  group  of  sen- 
tences, may  be  used  to  develop  any  scheme  of  cases  one  may 
wish  to  employ.     For  illustration,  take  the  following  group: 


PRACTICAL   LESSONS.  47 

1.  A  man  drank  water. 

2.  A  horse  threw  the  man. 

3.  A  man's  liat  is  hirge. 

4.  A  boy  spoke  to  the  man. 

5.  Joseph  is  a  7nan. 

1.  Question  upon  the  meaning  (in  the  domain  of  "what") 
until  the  details  are  distinct  and  the  words  are  lost  sight  of. 

2.  Que.stion  by  comparing  till  the  cases  or  several  uses  of 
man  are  distinct. 

3.  Parallel  each  case  with  a  group,  as  follows: 

1.  A  man  drank  water. 

2.  A  Jiorse  drank  water. 

3.  A  coiv  drank  water. 

1.  A  horse  threw  the  man. 

2.  A  horse  threw  the  boy. 

3.  A  horse  threw  the  lady. 

1.  A  man's  hat  is  large. 

2.  A  lady's  hat  is  large. 

3.  A  giant's  hat  is  large. 

1.  A  boy  spoke  to  the  man. 

2.  A  boy  spoke  to  tiie  horse. 
2.  A  boy  spoke  to  the  driver. 

1.  Joseph  is  a  man. 

2.  Henry  is  a  boy. 

3.  Carlo  is  a  dog. 

And  from  these  groups  lead  the  pupils  to  assimilate  what  con- 
stitutes each  case. 

It  is  not  deemed  necessary  to  add  further  illustrations  in 
this  subject,  as  those  given  are  a 'fair  type  of  all  grammar 
work. 


48  PEDAGOGICS, 


GEOGRAPHY. 


In  this  subject  intellect  is  occupied  more  in  perceiving  than 
in  any  other  process,  as  the  number  of  data  necessary  to 
arrive  at  a  truth  are  so  much  more  numerous  in  most  cases 
than  in  other  subjects. 

In  general  the  principles  that  affect  the  life  or  character 
of  a  pupil  are  not  assimilated  until  after  the  period  of  school 
life  has  expired.  For  illustration:  A  man  is  a<ked  to  leave 
his  home  and  become  a  citizen  of  another  country  or  province 
of  his  own.  Now  the  data  he  has  in  reference  to  that  country 
or  province  constitute  the  "  whole"  that  contains  the  princi- 
ple or  truth  which  is  to  determine  a  course  of  so  much  inter- 
est to  himself  and  family.  Upon  his  decision  rests  the  future 
happiness  and  prosperity  of  himself  and  those  dependent  on 
him.  In  like  manner  principles  that  govern  investments  of 
money,  ventures  in  commerce,  etc.,  etc.,  are  all  assimilated 
through  geographical  data  which  have  been  accumulating  in 
the  mind  since  early  childhood. 

Every  human  being  is  so  related  to  geographical  data 
that  any  great  success  in  life  is  impossible  of  attainment 
without  a  comprehensive  knowledge  of  the  subject. 

Its  importance  being  paramount,  then  it  folhnvs  that  the 
teacher  who  introduces  the  topic  to  a  child  should  adapt  his 
work  so  as  to  prepare  the  pupil  for  assimilations  that  will 
serve  him  well  when  he  needs  them. 

The  method  employed  in  geography  should  be  the  same 
as  has  been  illustrated  in  Arithmetic  and  in  Language.  It 
should  vary  in  detail  to  suit  the  peculiarities  of  the  subject, 
these  requiring  more  work  in  perceiving  and  comparwg  than  in 
asswillatlng.  Tiiere  are  many  assimilations  a  pupil  needs  to 
make  as  he  proceeds,  and  the  teacher  should  cause  him  to 
make  them  in  proper  order. 

"  The  world  is  my  home,"  should  be  among  the  first  assim- 
ilations made  by  one  properly  instructed  in  geography.     This 


PRACTICAL   LESSONS.  49 

assimilation,  though  it  may  be  made  imperfectly  at  first,  con- 
nects the  pupil  by  new  ties  to  the  eartli,  gives  him  an  inter- 
est in  its  study  that  will  never  flag  through  life,  keeps  alive 
his  attention,  energizes  his  memory  for  the  Herculean  task  of 
storing  away  the  countless  data  of  this  science,  and  rouses  his 
imagination  to  enter  upon  the  pleasing  task  of  constructing 
that  grand  concept  of  the  world  that  is  to  be  the  chief  means 
of  solacing  his  leisure  hours  spent  in  reading,  that  is  to  be 
the  vehicle  by  whicii  he  may  visit  distant  lands  while  quietly 
resting  at  home,  and  that  is  to  bring  success  to  his  ventures 
in  business. 

The  younger  the  chihlren  are  the  less  apt  will  they  be  to 
take  an  interest  in  the  study  of  geography  from  books  and 
maps,  for  the  reason  tliat  they  have  no  cares  upon  ihem  and 
do  not  understand  the  relations  in  which  they  stand  to  the 
world.  As  soon  as  thev  are  led  to  comprehend  that  all  they 
have,  and  all  they  will  ever  need  to  use  for  food,  clothing, 
and  shelter  are  won  by  hard  toil  Irom  nature's  stores,  and 
that  if  they  wish  to  have  periods  of  rest  and  enjoyment  dur- 
ing life  they  must  learn  nature's  secrets,  and  be  able  to  gain 
a  living  by  a  minimum  of  toil,  they  will  be  inspired  to  equip 
thenfselves  for  the  task  before  them  by  storing  up  geograph- 
ical knowledge. 

By  keeping  this  in  mind,  and  by  grouping  the  facts  of  the 
lesson  so  as  to  suggest  it,  even  young  children  may  be  im- 
pressed by  this  thought. 

Many  assimilations  requiring  special  lessons  and  extra  time 
devoted  to  them  aside  from  the  regular  text  lessons  are  nec- 
essary to  make  the  general  work  profitable  in  the  highest 
degree.     Such  are : 

(a)  "A  map  is  a  representation  of  a  part  or  the  whole  of 
the  earth's  surface." 

(6)  *'The  ocean  is  the  great  source  of  all  life." 
(c)  ''Life  thrives  where  climate  permits  and  where  sus- 
tenance abounds." 

4 


50  PEDAGOGICS. 

(d)  "  Climate  depends  upon  latitude,  elevation,  prevailing 
winds,  and  contiguous  ocean  currents." 

(e)  "Population  follows  natural  highways." 
(/)  ''Cities  are  built  upon  rivers  or  coasts." 
(^)  "Mines  are  found  in  mountainous  sections." 

Qi)  "  Manufactories  and  mills  are  located  upon  streams 
having  natural  waterfalls." 

(i)  "An  indented  coast  line  is  favorable  to  commerce." 

A  correct  method  in  geography  requires  that  the  whole  of 
the  instruction  should  be  founded  upon,  and  the  detached 
facts  be  learned  by  the  light  shed  upon  them  by  a  series  of 
general  truths  such  as  are  given  above.  These  are  not  given 
as  a  complete  series,  but  as  illustrative  of  the  utility  of  such 
work.  Thousands  of  facts  in  geography  will  be  learned  with 
great  facility  if  the  general  truth  of  which  each  is  a  species 
is  known  beforehand,  and  these  same  facts  will  be  remem- 
bered with  much  greater  ease. 

Suppose,  for  illustration,  the  following  texts  are  encoun- 
tered:* 

"  Arabia  is  chiefly  a  hot,  desert  plateau  with  oases  of  different 
sizes,  in  which  dates,  grapes,  tamarinds,"  and  other  fruits  grow.  It 
has  no  general  government,  the  inhabitants  being  ruled  by  sheiks 
or   chiefs." 

"The  Empire  of  Japan  consists  of  islands  which  contain 
mountains,  streams,  forests,  and  a  well-cultivated  soil.  The  prin- 
cipal occupations  of  the  Japanese  are  agriculture,  manufactur- 
ing, and  mining.  Its  exports  comprise  tea,  rice,  silks,  porcelain, 
fans,  and  lacquered  ware." 

-:i:-  *  *•  *  -;K-  *■  *-  *  -:•:■  -:;:•  -:•:-  * 

"  Kentucky  is  about  half  the  size  of  Kansas.  Its  surface  is 
mostly  hilly,  and  slopes' toward  the  northwest.  The  southeastern 
part  is  mountainous.  In  production  of  tobacco,  hemp,  and  flax 
Kentucky  surpasses  every  other  State  in  the  Union,  The  "blue- 
grass"  region,  in  the  basins  of  the  Licking  and  Kentucky  rivers, 
is  celebrated  for  fine  horses.  Louisville,  at  the  Falls  of  the  Ohio 
River,  is  the  most  important  tobacco  market  in  the  country." 

*  These  extracts  are  copied  from  Barnes'  Complete  Geograph5\ 


PRACTICAL   LESSONS.  51 

A  great  many  facts  are  embraced  in  these  three  extr.icts. 
The  text-book  from  which  they  are  taken  contains  nearly  one 
hundred  pages  of  similar  matter.  Is  it  too  much  to  know? 
Can  one  be  said  to  be  educated  in  geography  unless  he  knows 
much  more  than  is  given  here  of  each  of  one  hundred  coun- 
tries and  important  provinces?  Can  we  expect  to  teach  it 
all  as  detached  matter  ? 

The  answers  to  these  questions  are  obvious,  and  suggest  a 
method  founded  upon  ammilations  for  general  principles,  and 
patient  filling  in  by  adding  to  the  original  "wholes"  from 
which  assimilations  were  made  the  new^  facts  as  they  are  per- 
ceived after  comjMring  them  with  the  original  data. 

To  illustrate  the  method  suggested  : 

Suppose  a  class  to  have  already  assimilated  the  truths 
marked  above  as  (a),  (b),  (c),  etc.,  etc.,  would  they  not  be 
much  more  apt  to  remember  what  is  said  about  Louisville, 
about  the  government  of  Arabia,  and  about  the  occupations  of 
the  Japanese  and  their  exports  f 

Is  there  any  fact  in  either  of  the  extracts  that  is  not  a 
species  of  one  of  the  general  truths  given.,  or  of  some  other 
important  one  in  a  full  series?  Would  not  a  pupil  so  in- 
structed, after  reading  what  is  here  given,  even  if  his  text- 
book omitted  the  facts,  be  able  to  say  confidently :  "  There 
are  large  cities  in  Japan,  but  not  in  Arabia?"  Would  he 
not  also  be  able  to  say  that  Louisville  is  a  manufacturing 
city,  and  that  the  people  of  the  "bluegrass  region"  are 
wealthy,  cultured,  and  inclined  to  field  sports? 

Are  there  not  other  facts  of  the  countries  mentioned  which 
are  indissolubly  linked  with  those  given  in  the  extracts,  and 
which  would  be  readily  appropriated  by  a  mind  prepared  for 
the  task  ? 

Directions  are  given  below  as  to  how  to  prepare  '*  wholes" 
for  the  assimilation  of  general  truths  as  a  basis  for  after- 
study. 

1.  A  proper  *'  whole"  for  making  the  assimilation,  "A  map 
is  a  representation  of  a  part  of  the  earth's  surface,"  is  the  con- 


52  PEDAGOGICS. 

struction  by  the  pupil  of  one  or  more  maps  of  yome  region  or 
district  with  which  he  is  familiar.  Wiien  he  has  done  this 
with  the  teacher's  aid,  and  has  used  the  same  conventional 
signs  on  his  map  that  are  used  in  his  text  book  to  mark  rivers, 
lakes,  mountains,  etc.,  he  is  ready  to  get  ideas  from  the  maps 
in  his  book.* 

2.  •'  The  ocean  is  the  great  source  of  all  life." 

Take  for  a  "  whole"  the  elements  that  contribute  to  sup- 
port life  in  animals  and  plants.  Appeal  to  the  pupils'  ex- 
periences as  to  what  terminates  and  prolongs  life.  The  steps 
are  easy  to  the  assimilation  mentioned. 

3.  *'  Life  thrives  where  climate  permits  and  sustenance 
abounds." 

Take  for  a  "  whole  "  the  cities  (abodes  of  men)  in  United 
States,  Mexico,  Central  America,  Dominion  of  Canada,  and 
(?)  Greenland. 

Compare  as  to  population,  etc.,  etc. 

Ask  ivhy  the  facts  are  so,  and  the  assimilation  is  made. 

Plants  and  animals  of  different  regions  in  North  America 
can  be  compared  to  make  the  same  assimilation. 

4.  "  Cities  are  built  upon  rivers  or  sea-coasts." 

Make  a  "  whole"  of  the  locations  of  large  cities  on  the  map 
of  North  America,  and  from  it,  by  questioning,  get  the  assimi- 
lation. 

Enough  examples  have  been  given  to  illustrate  how  readily 
this  work  may  be  done. 

The  continents  ought  to  be  studied  one  at  a  time,  and  the 
principles  referred  to  ought  to  be  taught  from  the  details  of 
the  first  continent,  as  thoroughly  as  possible. 

Such  "wholes"  as  are  given  below  should  be  used  for 
reviews,  the  details  to  be  supplied  from  memory  by  the 
pupils: 

*  However  perfect  may  be  the  maps  of  a  text-book,  they  will  not  suffice  to 
illustrate  fully  such  texts  as  have  been  quoted  above.  Relief  maps  of  conti- 
nents are  a  necessity  for  the  best  instruction.  These  can  be  made  by  a  teacher, 
using  paper  pulp  or  putty,  or  some  other  plastic  material  for  the  elevations. 
Fine  maps  of  this  character  are  now  made  for  sale. 


PRACTICAL   LESSONS.  53 


CUBA. 

Gulf  of  Mexico — Florida — Spain — Havana — Matanzas — 
oranges —  lemons — tobacco —  sugar — mahogany — rosewood — 
Columbus — 1492 — hurricanes — Spaniards — Negroes,  etc.,  etc. 

After  these  details  are  arrived  at,  the  general  direction  be- 
ing, "  Put  down  what  Cuba  makes  you  think  of" — as  a  class 
exercise — and  arranged  logically,  have  the  class  write  up  the 
geography  of  the  island. 

These  "wholes"  may  be  made  of  many  topics,  as  Amazon, 
Andes,  cotton,  rice,  coal,  Caucasian  race,  etc.  They  serve 
admirably  to  put  knowledge  in  a  classified  form  into  the 
memory. 

Many  new  words  are  brought  into  the  vocabulary  by  the 
study  of  geography.  The  requirements  of  Postulate  IV,  as 
well  as  illustrations  under  Reading  in  this  Monograph,  make 
it  certain  that  a  teacher  should  have  the  geography  read  by 
the  pupils,  and  not  recited  from  memory,  as  was  the  universal 
method  not  many  years  ago.  In  other  words,  there  ought  to 
be  no  reciting  of  answers  with  books  closed,  and  maps  hid, 
except  in  review  lessons,  illustrated  above. 


ETHICS. 

At  the  foundation  of  right  doing  lies  right  thinking. 
Every  member  of  society  stands  in  certain  relations  to  his 
fellows,  and  certain  duties  are  incumbent  on  him.  These 
duties  are  two-fold,  viz.,  To  individuals  and  to  the  whole. 

To  fulfill  any  duty  marks  a  man  as  possessing  the  virtue 
that  is  its  fulfillment.  Honesty  is  a  virtue  that  will  inhere  in 
any  individual  who  respects  the  property-rights  of  others. 
And  so  for  all  virtues.  Now  is  it  important  to  instruct 
young  persons  in  ethics?  And  can  it  be  done  without  teach- 
ing the  tenets  of  any  church  ? 

No  one  who  has  observed  the  growth  of  the  money-getting 


54  PEDAGOGICS. 

feeling  in  this  country,  who  has  observed  its  ruthless  hand 
corrupting  legislation,  defiling  religion,  and  grinding  poverty, 
can  for  a  moment  deny  that  something  ought  to  be  done  to 
rescue  us  from  that  state  into  which  we  are  drifting,  a  state 
in  which  the  only  tie  that  shall  bind  us  is  that  weak  one 
known  as  "  honor  among  thieves." 

The  church,  or  rather  churches,  of  the  land  ought  to  see  to 
it,  while  they  have  the  power  over  public  opinion,  that  ethics 
is  introduced  and  taught  in  the  common  schools.  This  is 
the  only  means  by  which  all  classes  can  be  reached.  No 
other  influence  extends  to  every  home  in  the  land. 

The  necessity  for  teaching  ethics  being  apparent,  and  the 
medium  through  which  enlightenment  is  to  come  provided, 
it  only  remains  to  agree  upon  the  curriculum  and  the 
method. 

No  church  prejudices  can  be  offended  if  the  teachers  make 
the  dictionary  the  basis  of  their  work.  By  this  simple 
means  all  contentions  can  be  quieted,  and  the  good  work  of 
training  the  youth  of  our  land  morally,  be  consummated. 

Man,  "created  in  God's  image,"  is  a  progressive  being, 
and  inherits  a  tendency  to  admire  the  beautiful,  to  recognize 
the  true,  and  to  retain  the  good.  If  noble  ideals  are  ])laced 
before  him,  and  connected  with  his  daily  walk,  he  will  strive 
to  reach  them  and  gradually  realize  them. 

The  experiences  of  a  race  in  conduct  record  themselves  in 
the  vocabulary  of  that  race  in  the  names  for  virtues  and  vices. 
Now,  if  the  teacher  will  but  give  lessons  upon  these  ab- 
stract terms,  he  will  be  laying  the  foundation  for  correct  con- 
duct. If  the  same  pains  were  taken  in  school  to  acquaint  the 
children  with  the  meanings  of  honesty  and  fortitude  as  are 
taken  to  teach  exponent  and  predicate  nominative,  the  results 
in  ethics  would  be  similar  to  the  results  in  science. 

Postulate  IV  assumes  that  words  must  be  made  generic  in 
meaning  to  the  child  to  be  in  any  high  degree  useful  to  him. 
Now,  to  make  any  word  generic  in  mind,  its  full  range  of 
meaning  must  be  brought  to  consciousness,  and  comparison 


PRACTICAL   LESSONS. 


55 


o"2«^:3  2.     ^    ^ 


lat  approach  it  in  meaning, 
tosite  in  meaning, 
aching  the  virtue  expressed 
below. 


i-&.'^£^lg^     >  ORTITUDE. 


:?^i     §^o|g.    g  and 

jfio      ^p'^^^i"^    2  nder  financial  reverses. 

a-^       t^  oq   B  ^  H-  ^      W  3h, 


giS^^s   Q  id 


S.£:     S^i...  3Qg.^    o  .    ,3f  a  limb. 

^^     ^^^l"i    ^  's.    Garfield,    Joan  d'  Arc, 

^1      §^§12^'-^    E  imozin,  Jesus  Christ,  Casabi- 


EE  s  ^  ?-2  ^.'/5  p  read  to  the  class.     Compare 

»g:  Si^'^^^a^E  S*  courage,  bravery,  endurance, 

q  J?  ^  g.M§  ^-^  S  rs  possessing  like  qualities. 

11  o^^^ii  R  ualities 
o 


•midity,  hesitation,  fear,  treach- 


early  every  case  a  pupil  will 

r^  ^     «>^.®.^  ^^    »  «e  a  man  or  woman  of  forti- 

^  ^      £  c  ^^.c  ^    o  •  almost  certainly,  to  assimi- 

§|^S-g^*3-3|  f  the  teacher  will  but  take 

^^     I  §^  ll  S^   ?  imples  oi'  fortitude  that  have 

&^§      S^'S  tf  §^J3  i    ^  f  he  can  bring  these  to  the 

^Ig'    S-Bi-^o-s    i,  ibited  in  their  own  conduct, 

^^      o^^Sis^^S  changing  the  current  of  their 


2°     =?o  ^  §  ^    i-  a"y  ^^"^^^  a^^  necessary,  and 

p-     =f  P  7  ^  ?r.^  I  lasting  impression. 

pies  observed  by  them,  and  if 
on  the  subject  of  any  lesson, 
1  that  they  have  learned  the 
begin  to  exhibit  in  their  con- 


54  PEDAGOGICS. 

feeling  in  this  country,  wh 
corrupting  legislation,  defilii 
can  for  a  moment  deny  thai 
rescue  us  from  that  state  ir 
in  which  the  only  tie  that 
known  as  "  honor  among  th 

The  church,  or  rather  chi 
it,  while  they  have  the  pow' 
is  introduced  and  taught  i 
the  only  means  by  which  i 
other  influence  extends  to  e 

The  necessity  for  teach  ir 
medium  through  which  enl 
it   only    remains   to   agree 
method. 

No  church  prejudices  car 
the  dictionary  the  basis  o 
means  all  contentions  can  b 
training  the  youth  of  our  la 

Man,  "  created  in  God's 
and  inherits  a  tendency  to  i 
the  true,  and  to  retain  the  ^ 
before  him,  and  connected  ^ 
to  reach  them  and  gradually 

The  experiences  of  a  race 
the  vocabulary  of  that  race  i 
Now,  if  the  teacher  will  I 
stract  terms,  he  will  be  layir 
duct.  If  the  same  pains  we. 
children  with  the  meanings 
taken  to  teach  exponent  and 
in  ethics  would  be  similar  to 

Postulate  IV  assumes  tha 
meaning  to  the  child  to  be  u 
Now,  to  make  any  word  ge 
meaning  must  be  brought  • 


PRA.CTICAL   LESSONS.  55 

of  it  must  be  made  with  others  that  approach  it  in  meaning, 
and  with  others  still  that  are  opposite  in  meaning. 

An  outline  of  a  *'  whole"  for  teaching  the  virtue  expressed 
by  the  word  Fortitude  is  presented  below. 

EXAMPLES   OF   FORTITUDE. 

(a)  A  woman  burying  her  child, 

(6)  Sending  her  son  to  battle,  and 

(c)  Comforting  her  husband  under  financial  reverses. 

(c?)  A  soldier  on  a  forced  march, 

(e)  Confronting  the  enemy,  and 

(/)  Suffering  the  amputation  of  a  limb, 

(g)  Historical  examples:  Mrs.  Garfield,  Joan  d' Arc, 
Washington,  Marshal  Ney,  Guatimozin,  Jesus  Christ,  Casabi- 
anca,  etc..  etc. 

Let  these  examples  be  told  or  read  to  the  class.  Compare 
them  with  examples  of  strength,  courage,  bravery,  endurance, 
resolufeness,  persistence,  and  others  possessing  like  qualities. 
Compnre  also  with  examples  of  timidity,  liesiiation.Jear,  treach- 
ery, and  others  having  opposite  qualities. 

If  this  work  is  well  done,  in  nearly  every  case  a  pupil  will 
be  inspired  with  a  desire  to  become  a  man  or  woman  of  forti- 
tude. Moreover,  he  may  be  led,  almost  certainly,  to  assimi- 
late a  principle  for  guiilance,  if  the  teacher  will  but  take 
pains  to  add  to  the  "  whole  "  examples  offortitude  that  have 
been  exhibited  by  children.  If  he  can  bring  these  to  the 
memory  of  the  children,  as  exhibited  in  their  own  conduct, 
he  is  almost  sure  to  succeed  in  changing  the  current  of  their 
lives. 

Repetitions  of  the  work  with  any  word  are  necessary,  and 
also  tests  in  order  to  be  sure  of  a  lasting  impression. 

If  pupils  can  point  out  examples  observed  by  them,  and  if 
they  can  construct  an  essay  upon  the  subject  of  any  lesson, 
no  better  evidence  can  be  given  that  they  have  learned  the 
meaning  of  the  term.     If  they  begin  to  exhibit  in  their  con- 


56  PEDAGOGICS. 

duct  an  example  of  a  virtue  taught  tliem,  it  is  proof  positive 
that  they  have  assimilated  a  rule  for  action. 

Note.— The  manner  of  giving  such  lessons  ;is  has  been  outlined  here,  is 
more  elaborately  treated  under  Character  Education.  The  nature  and  value  of 
the  "Hypothetical  Discourse"  in  teaching  right  conduct  is  there  illustrated 
fully. 


ALGEBRA. 

The  authors  understand  that  what  is  written  here  concern- 
ing algebra  is  but  part  of  arithmetic.  Hence  it  ought  to  be 
taught  as  such  and  at  tlie  same  time  with  arithmetic.  The 
use  of  a  letter  to  represent  any  number  seems  as  simple  as 
the  use  of  any  class  name,  and  is  as  easily  learned  by  the 
average  pupil. 

In  the  review  of  Principle  (2)  of  Arithmetic  (see  page  24), 
the  use  of  any  number  of  things  as  a  unit  should  be  made 
very  familiar  to  the  pupil.     There  he  learns  that 

3,  4sts.  -f  5,  4  sts.  -f  6,  4  sts.  =  14,  4  sts. 

Such  examples  as: 

5,  3  sts.  4  6,  5  sts.  +  5,  8  sts.  +  5,  9  sts.  =? 
should  be  given  the  pupil,  expecting  him  to  apply  Principle' 
10  (see  page  24),  and  write: 

3,  5  sts.  -f-  6,  5  sts.+  8,  5  sts.  +  9,  5  sts.  =  26,  5  sts 
The  units  and  coefficients  should  finally  reach  up  into  the 
thousands.     The  transition  to 

3,  a  sts-.  +  6,  a  sts.  -f-  8,  a  sts.  +  9,  a  sts.  =  26  a  sts.. 
is  simple  and  is  easily  made.  To  this  end  vary  the  number  of 
things  in  the  unit  while  the  coefficients  remain  the  same; 
thus  by  resemblances  disclosing  the  same  demand  for  a  class 
name  for  the  number  of  things  in  the  unit  as  for  any  object, 
as  chair. 

The  use  of  this  method  in  subtraction,  as  in  Principle  11 
(see  page  25),  will  familiaiize  the  pupil  with  the  use  of  let- 
ters as  names  for  any  number. 

In  arriving  at  Principle  10^  (see  page  24),  the  following 
steps  are  safe.    By  Principle  10;  6,  12  sts.  ==  12,  6  sts.,  omit 


PRACTICAL    LESSONS.  57 

ting  the  things  6  ■  12  =  12  •  6  (1).  So,  also,  3,  2  sts.  =  2,  3 
sts.,  omitting  the  things  3  2  =  23.  So,  also,  3,  4  sts.  =  4, 
3  sts.,  3-4=43.     Substitute  in  (1)  and  we  have  : 

3  2  3  4  =  4  3  2  3  =  4  •  2  3  •  3,  etc.  Doing  likewise 
with  4  and  we  have :  3-2-3-2-2  =  2-22-33  =  72. 
Having,  by  repetitions,  establi.-^hed  Principle  10',  then  exer- 
cise the  class  thoroughly  thus:  What  and  how  many  prime 
factors  are  in  12?  in  8?  in  17?  in  54?  etc.  Speak  of  8  as 
having  three  2's  as  factors;  of  12  as  having  two  2's  and  one 
3  as  factors,  etc.  Ask  at  the  same  time  for  the  number  of  2's 
as  units  in  8,  in  12,  etc.  Wiite  on  tlie  board  2  +  2+  2  +  2=4, 
2's  =8,  and  2  •  2  •  2  =  8.  Do  the  same  with  12^  16,  24,'  etc. 
If  the  attention  of  the  pupil  is  called  to  use  of  4  in  4,  2's,  and 
the  question  asked,  why  not^ise  a  figure  to  express  the  number 
of  2's  as  factors  in  8,  16,  32,  etc.,  pupils  find  no  difficulty  in 
appreciating  the  need,  and  are  prepared  for  2  2  •  2  =  2'^  =  8, 
etc.  Now  ask  for  the /actors  of  the  product  of  12. and  24 
without  knowing  the  product,  and  pu])ils  easily  write  12  •  24  = 
2  •  2  •  3  X  2  •  2  •  2  •  3,  and  applying  Principle  10',  we  have 
12  •  24  =  2  2  2  2  3  3  =  2*  •  3^ ;  with  which  result  parallel 
12  +  24  =  6,  2's  -f  12,  2's  =  18,  2's,  and  12  •  24  =  2^  •  3  x 
2"'  •  3  =  2"  •  3"^  and  the  average  pupil  has  discovered  for  him- 
self the  principle  that  exponents  of  like  factors  are  added  in 
multiplication.     Place  on  the  board  such  examples  as: 

24  X  36  X  72  X  96  X  48  X  144  =  ? 

and  ask  for  the  factors  of  the  product  without  finding  it.  On 
the  board,  after  pupils  find  it,  write: 

24      X  36       X  72       X  96     X  48      x  144  =  2^'   3». 
2»  3  X  2^  3^^  X  23  32  X  2^  3  X  2*  3  X  2*  3^. 

Then  : 

a'b'  c'd'  X  aH'd'  x  a'c'd'  x  cM*=  ? 

and  others.    Then  : 

a«*  6^«    X  a^  6'"    =  ? 
^864  ^565  X  ^m  5796  ^  V. 


58  PEDAGOGICS. 

and  others  of  like  kind,  ending  the  group  with  a*"  6"  x  a^  6'  =  ? 
and  after  a  little  repetition  nearly  all  will  readily  do  such  ex- 
amples as : 

Then  give  such  a  group  as  follows : 

a'H''^   X  ab=  ?  '» 

^569^999  X  ab  =  ? 

and  others,  ending  with  a*"  6"  X  ab  =?  and  a  majority  will  be 
able  to  work  the  last  example.  The  greatest  care  must  be 
exercised  throughout  the  whole  of  such  work  to  let  the  })upil 
discover  for  himself  the  results,  and  how  as  well  as  w^hy  it  is 
so.  It  is  not  necessary  to  call  the  attention  of  the  reader  to 
the  application  of  the  various  postulates  in  the  work  given 
here. 

In  order  to  lead  the  pupil  to  discover  for  himself  the  mul- 
tiplication of  polynomials  the  following  "whole"  is  sug- 
gested: Let  the  pupil  multiply  46  by  68,  and  then  put  on 
the  board  as  he  answers  the  various  questions:  "What  are 
the  parts  of  46?"     "  \Yhat  are  the  parts  of  68?"  etc. 

46=  40-f  6=  22-10-f2  -8, 

68=  60-f  8=  2-3  -10+       2« 

"^)8=  320  +  48=  +2»-10-f2*-3 

276  =2400-f  360         =2^  •  3  •  10^-f  2^  •  3^  •  10 

'  3128=24^0-f  680+48=2^  •  3  •  102+2^  •  3^  ■  10  +  2^  •  10-f2*  •  3 

A  few  repetitions  of  this  "  whole"  will  enable  the  pupil  to 
work  with  ease  such  examples  as: 

(^ar  b""  -f  a''  ¥)  x  (a^  b^  +  a  ¥)  =  ? 

It  will  be  observed  that  the  use  of  the  "  10,"  as  above  in- 
dicated, will  gain  two  ends,  viz:  (1)  Make  the  pupil  familiar 
with  the  scale  of  tens,  and  (2)  make  the  teaching  of  division 
of  polynomials  easy. 

In  order  to  enable  the  pupil  to  arrive  at  the  meaning  of 

m 

a«  proceed  thus  :   Ask  what  does  §,  12  mean  ?    Pupil  answers, 


PRACTICAL   LESSONS.  59 

Separate  "  12"  into  three  equal  parts,  and  take  two  of  these 
parts  as  units.  12  =  4  +  4  -f  4  .-.  §,  12  =  4  +  4  =  2,  4's 
—  8.  Then  ask:  "  What  does  8^  mean?"  A  few  pupils  an- 
swer immediately  without  any  repetition,  Separate  8  into  three 
equal  factors,  and  take  two  of  them  as  factors.  Repetition 
will  enable  nearly  all  pupils  to  arrive  at  same  result.  Place 
on  board  after  pupils  have  solved  them : 

S^=2^  :  16^  =  2»  :  etc. 

8    =2- 2 -2  :16    =2-2-2-2:  etc. 

and  ask  what  a" means.  To  assure  results  write  a  =  6"  and 
6"*  =  c,  and  ask  pupils  what  ««  equals.    Use  such  examples  as  : 

3  3  .3 

2'^?     (2^)  =  ?     (2^0=?  freely. 

Teaching  division  of  monomials  is  an  easy  matter.  Space 
forbids  details  ;  the  results  arrived  at  below  will  indicate  pro- 
cesses. Remember,  pupils  must  arrive  at  results  for  them- 
selves. Ask  pupils  to  find  all  the  exact  divisors  of  12  by  the 
vse  of  factors,  and  when  they  have  done  the  work  place  on  the 
board  as  follows,  calling  attention  to  the  names  of  the  parts  : 


Divisor.     Quotient. 

Multiplicand 

.  Multipl: 

2     =2   3 

r 

2 

X2   3 

Dividend. 

2-2     =      3 

Product. 

2-2 

X      3 

12- 

-  i 

2   3     =      2 

12=  ^ 

2   3 

X      2 

2   2   3 

3     =2-2 

3 

X2   2 

^  2 

•2-3     =      1 

.2 

2-3 

X      1 

Then  ask  pupils  to  do  likewise  with  24,  36,  etc.  Then 
place  on  the  board  such  examples  as : 

r  2'  •  3  •  5^  =  ?  f  2^  •  3  •  5»  X  ? 

I   23- 3^ -53  =  ?  I   23- 32 -53  X? 

23.H*.5^_^^         3^-5^  =  ?  23-3*-5^=<;         3»-5^x? 

I   2^  ■  3*  •  5^  =  ?  I   2'  •  3*  ■  5'  X  ? 

t        5'       =?  15^        X? 

After  repetition  with  figures  use  letters  freely  both  as 
factors  and  exponents. 

To  teach  division  of  polynomials,  reverse  process  of  teach- 
ing multiplication. 


60  PEDAGOGICS. 

In  subtraction,  after  pupils  have  read  up  their  notes  on  the 
subject,  give  them  two  numbers,  such  as  57  and  96,  and  let 
the  pupils  compare  them  as  found  in  their  notes.  After  repe- 
tition, if  necessary,  put  on  the  board  as  follows: 

(+  96)  -  (+  57)  =  4-  39  (+  a)  -  (+  6)  =? 

(+  96)  -  (-  57)  =  -f  153  (+  a)  -  (-  b)  =? 

(_  96)  -  (+  57)  =  -  153  (-  a)  -  (-1-  b)  =? 

.  (_  96)  -  (-  57)  =  -  39  (-a)  -  (-  b)  =? 

(+  57)  -  (+  96)  =  -  39  (+  6)  -  (+  a)  =? 

(+  57)  -  (-  96)  =  +  153  (-f  b)  -   (-  a)  =? 

(_  57)  _  (4-  96)  =  -  153  (-  b)  -  (+  a)   =? 

(_  57)  _  (_  96)  =  -f  39  (-  b)  -   (-  a.)  =? 

and  require  pupils  to  write  answers  in  parentheses  thus: 
-f  (a  —  6),  +  (a  -f  6),  —  (a  -\-  b),  etc.,  having  informed 
them  that  the  number  "a"  is  greater  than  the  number  "6." 
Some  pupils  will  do  the  work  without  difficulty.  Repetition 
with  large  numbers  will  call  the  attention  of  the  pupils  to 
what  they  do  and  how  they  do  it.  If,  then,  a  few  pupils 
remain  who  have  not  succeeded,  by  questioning  in  the  whq^, 
how,  and  why,  the  teacher  will  enable  all,  or  nearly  all,  to  do 
the  work  by  themselves. 

Announcing  the  proposition  that  John  has  five  debts  less 
of  six  dollars  each  than  James,  and  requesting  the  pupil  to 
compare  John  to  James,  will  enable  him  to  discover  that  the 
product  of  —  5  and  —  6  is  +  30. 

Let  the  pupil  be  led  to  make  the  following  "whole,"  and 
he  learns  when  trinomials  can  be  separated  into  two  binomial 
factors,  and  how  to  do  it: 

42  X  43  =(4  •  10  -f  2)  (4  •  10  +  3)=  4^  •  10^  -f  5  •  4  •  10+  6 
54  X  56  ==(5  •  10 +  4)  (5- 10 -h  6)=  5^10^+  10- 5  10  +  24 
78  X  79  =(7   10  +  8)  (7-10  +  9)=  7^102+  17- 7- 10  +  72 

When  three  or  four  of  these  are  done,  ask  pupils  to  use 
letters,  and  if  they  fail,  ask  them  to  observe  closely  what 
they  do  and  how  they  do  it,  and  continue : 


PRACTICAL   LESSONS. 


61  X  67  =(6   10+  1)  (6   10  +  7)=  62-102+   8- 6   10+  7 
39  X  33  =(3   10  +  9)  (3   10  +  3)=  32- 10^ +12  •  3- 10 +27 

Then  many  pupils  will  generalize  thus: 

(a -10  +  6)  (a -10  +  c)=  a^  10» +(6  +  c)  a  •  10  +  6c. 

Those  who  fail  can  generally  be  brought  by  questioning  in 
detail  as  to  what,  how,  and  why  to  reach  the  desired  result. 
Then  put  x  for  10  and  get : 

{ax  +  6)  {ax  -{-  c)=  a^  x^  -\-  (b  -\-  c)  ax  +  be. 

In  applying  this  result  proceed  as  follows :  place  on  the  board 

r 


a'x''  +  10aa;  + 


l 


and  request  the  class  tofin-i  third  terms,  and  factor  resulting 
polynomials.  Some  will  do  this  work  without  any  more 
teaching.  With  others,  for  relation  of  10  and  the  third  term, 
call  attention  to  6  +  c  and  be  in  the  general  expression,  and 
lead  them  to  do  as  follows : 


10: 


Then  after  the  same  manner  place  on  the  board : 


f   9  +  1 

9x1=    9^ 

8+2 

8   X  2  =  16 

7+3        , 
6  +  4    ^"^ 

7   X  3  =  21 

^  The  third  terms 

6   X  4  =  24 

desired. 

5+5 

5l  X  5  =  25 

l¥  +  l 

¥  xf  =  ^J 

■ 

a'x'  -i- 


►  ax  +  36 


and  ask  pupils  to  supply  coefficients  of  second  term,  and  fac- 
tor the  results.  A  few  repetitions  serve  to  familiarize  the 
pupil  with  the  work. 


62 


PEDAGOGICS. 


Put  on  a  table  two  piles  of  40  straws  each,  and  let  the 
class  write  up  on  their  pads,  verifying  the  result  by  inspection 
of  the  straws  : 

2,  40  sts.  =  80  sts. 

Then  opposite  each  pile  place  two  piles  of  19  each,  with  2 
straws  to  the  left  of  each  pair  of  19's.  Then  lead  the  pupils 
to  write  up  the  result  as  follows,  verifying  as  before : 

2  (2  sts.  +  2, 19  sts.)  =  80  sts. 

Then  with  other  straws,  for  each  19  arrange  three  piles  of  5 
straws  each  with  a  pile  of  4  to  the  left  of  each  group  of  three 
5's.     As  before  lead  the  pupil  in  verifying  and  writing  up,  as 

follows : 

2  [2  sts.  +  2  (4  sts.  +  3,  5  sts.)]  =  80  sts. 

With  another  80  straws  make  an  arrangement  based  on 
the  last  result  by  separating  the  5's  into  piles  of  3  and  2,  and 
arrive  at  the  following  arrangement  of  straws  : 


I  I 


I  I  I  I 


I  I  I  I 


I 


I    i 

I    I 
I    I 


I    I 


I  I 


n  I  I  I 


I  I  I  I 


I  I 
I  I 
I  I 
I  I 
I  i 
I  I 


Pupils  when  asked  will  generally  succeed  in  wri 
the  result,  which  is  as  follows : 


ing  up 


80  sts. 


2  I  2  sts.  +  2  [4  sts.  4-  3  (3  sts.  +  2  sts.)]  1  = 

If  any  fail  to  do  so  repetitions  will  assure  success. 
Continue  in  repetitions  by  making  arrangements  of  straws 
that  will  give  such  results  as  follows : 

3  j  2  sts.  +  2  [3  sts.  4-  5  (4  sts.  +  1  st.)]  l  =  174  sts. 


PRACTICAL   LESSONS.  63 

Reverse  the  process  by  giving  a  parenthetical  expression, 
thus : 

2^3sts.  +  2  I  4  sts.  +  2  [5  sts.  +  3  (2  sts.  +  3  sts.)]  j  )  =  182  sts. 

And  require  the  pupils  to  arrange  the  straws  to  correspond. 

GEOMETRY. 

The  intention  in  these  remarks  on  teaching  geometry  is 
only  to  introduce  the  subject  and  indicate  the  manner  of  ap- 
plication of  the  postulates. 

Prepare  a  number  of  similar  rectangles  cut  out  of  paste- 
board. Give  each  pupil  three  or  four  of  these  rectangles,  and 
one  not  similar  to  them.  The  three  or  four  similar  rectangles 
constitute  a  "whole."  The  pupil  is  expected  (1)  to  discover 
in  what  respects  they  resemble  each  other ;  (2)  to  discover 
the  principle,  a  content  of  these  resemblances,  that  "  Rect- 
angles whose  sides  are  equimultiples,  when  placed  on  each 
other  properly,  will  have  their  free  corners  in  the  same 
straight  line."  It  would  be  well  to  have  a  five-sided  figure 
in  full  view  of  the  class.  Pupils  will  generally  write,  in  ef- 
fect, as  follows:  *' These  four  pieces  of  pasteboard  resemble 
in  having  four  sides,  four  square  corners,  and  in  being  longer 
than  they  are  wide.  They  differ  in  the  lengths  of  their  sides." 
A  few  questions  in  the  what  will  develop  in  their  minds  that 
they  resemble  in  having  opposite  sides  the  same  length,  and 
equally  distant  apart  at  the  ends.  Ask  the  pupils  to  place 
the  rectangles  cornering  together  on  each  other,  and  the  fact 
that  the  free  corner  of  the  dissimilar  one  is  out  by  itself  will 
call  their  attention  to  the  fact  that  the  three  similar  rectangles 
have  tJieir  free  corners  in  the  same  line,  which  they  will  verify 
with  their  rulers,  and  announce  that  the  three  rectangles  re- 
semi)le  in   ''  pointing  in  the  same  direction." 

Take  the  odd  rectangle  from  them  and  ask  them  to  reduce 
the  three,  by  scales  given,  to  the  same  size  on  their  pads,  when 
they  will  discover  the  idea  that  their  sides  are  equimultiples. 


64  PEDAGOGICS. 

Then  ask  the  pupils  to  make  a  number  of  rectangles 
on  their  pads  with  sides  equimultiples.  Some  will  do  this 
by  drawing  the  diagonal  of  the  large  rectangle  and  make  the 
others  corner  on  it.  Others  will  take  two  numbers,  find  the 
equimultiples,  and  construct  the  rectangles. 

Now  ask  them  to  discover  how  many  times  a  smaller  rect- 
angle is  contained  in  a  larger,  and  they  will  generally  do  the 
work  with  ease.  Then,  by  comparing  results  in  numbers  with 
the  corresponding  common  multiplier,  they  discover  that  the 
former  is  the  square  of  the  latter.  Ask  them  to  explain  why 
this  is  so,  and  they  will  answer,  that  the  multiplier  tells  how 
many  of  the  smaller  rectangles  can  be  constructed  in  the 
larger  each  way,  the  product  of  which  numbers  gives  the 
whole  number  of  the  smaller  contained  in  the  larger,  because 
the  number  in  a  row  multiplied  by  the  number  of  rows  will 
give  the  whole  number.  Now  call  their  attention  to  the  fact 
that  the  square  of  any  number  is  contained  in  the  square  of 
any  multiple  of  that  number,  a  number  of  times  represented 
by  the  square  of  the  multiplier;  or,  referring  to  figures  pre- 
pared on  the  board,  show  the  same  thing  between  the  base  of 
the  smaller  rectangle  and  its  multiple,  the  base  of  the  larger 
rectangle,  and  they  arrive  at  the  principle  that  "The  ratio 
of  similar  rectangles  is  the  ratio  of  the  squares  on  correspond- 
ing sides." 

Ask  them  for  the  number  of  square  inches  in  a  rectangle, 
and  few  pupils  fail  to  answer:  "Multiply  the  number  of 
inches  in  length  by  the  number  of  inches  in  width."  Then 
they  can  readily  be  led  to  disvover  the  principle  that  "The 
ratio  of  similar  rectangles  is  the  ratio  of  the  squares,"  from  the 
fact  that  areas  are  products  of  bases  and  altitudes,  the  com- 
mon multiplier  entering  as  a  factor  in  both  length  and  width. 

Give  each  pupil  a  rectangle  and  a  parallelogram  of  equal 
bases  and  altitudes  (a  "whole"),  and  ask  for  resemblances 
and  differences,  and  the  average  pupil  will  readily  discover 
the  equality  of  areas  among  other  resemblances.  A  few 
questions  will  enable  all  to  discover  that  fact. 


PRACTICAL   LESSONS.  65 

Give  each  pupil  three  similar  parallelograms  cut  out  of 
pasteboard,  and  they  will  readily  discover  the  resemblances 
and  differences  as  they  did  with  the  rectangles,  etc. 

Give  the  pupils  similar  right  triangles  cut  out  of  paste- 
board, and  by  use  of  rectangles  they  readily  discover  relations 
and  areas,  etc. 

Give  the  pupils  similar  obtuse  angled  triangles,  and  they 
readily  discover  the  fiicts  as  above. 

The  serious  difficulties  of  the  pupils  begin  with  the  at- 
tempt to  discover  the  three  bases  and  their  altitudes  of  one 
obtuse  angled  triangle.-^  By  standing  the  triangle  on  any 
base  they  find  the  corresponding  altitude,  but  are  confused 
by  the  figure.  A  little  patience  with  three  separate  triangles 
will  enable  them  to  apply  the  principle  so  as  to  find  the  area 
of  one  obtuse  angled  triangle  in  the  three  modes. 

THE   ANGLE. 

It  is  hardly  necessary  to  premise  that  a  pupil  must  know 
what  "direction"  is  in  order  to  understand  the  "difference 
of  two  directions,"  which  is  an  angle. 

Ask  all  the  pupils  to  point  at  some  object  in  the  room,  and 
then  to  write  up  what  they  were  doing.  Then  ask  every 
pupil  to  point  in  the  direction  that  object  is  from  where  he 
sits,  and  let  them  *'  write  up"  that  act  also.  Then,  pointing 
in  some  direction,  ask  all  to  point  in  the  same  direction  that 
you  are  pointing,  and  write  up  that  also. 

Mark  two  points  on  the  board,  and  ask  one  pupil  to  make 
an  arrow  pointing  from  one  to  the  other  point,  and  another 
pupil  at  the  same  time  to  make  an  arrow  from  the  second 
point  to  the  first,  and  ask  all  to  write  up. 

Secure  a  number  of  long  pointers  ;  call  up  a  number  of 
boys  and  let  them  point  now  at  this  object  and  now  at  that, 
and  then  in  any  indicated  direction.     Place  two  boys  wide 

*Soine  pupils  overcome  this  diflftculty  by  constructing  the  three  parallelo- 
grams, of  which  the  triangle  is  half,  and  finding  the  three  bases  and  altitudes 
through  the  three  parallelograms. 

5 


66  PEDAGOGICS. 

apart  with  pointers;  ask  them  to  point  in  the  same  direction. 
Call  -up  a  third  and  fourth  to  point  in  the  same  direction. 
Ask :  ''Are  these  all  the  same  direction,  or  are  they  only 
pointing  in  the  same  direction  ?  " 

Make  a  number  of  points  on  the  board,  and  let  one  pupil 
elect  a  direction  for  his  arrow  ;  then  let  pupil  after  pupil 
make  arrows  from  other  points  in  the  same  direction ;  then 
ask  a  number  of  pupils  in  different  parts  of  the  room  to  give 
the  same  direction  with  pointers.  Ask,  again,  if  these  rep- 
resent the  same  direction  or  are  only  pointing  in  the  same 
direction. 

Starting  with  a  clean  board,  make  an  arrow  diagonally  up 
on  the  board,  and  ask  each  pupil  to  do  the  same  on  his  pad. 
Name  the  arrow  A,  with  letter  at  the  point.  Then  draw  an- 
other arrow  as  distant  as  practicable  in  the  same  direction  ; 
ask  pupils  to  do  likewise,  and  ask  pupils  to  name  this  direc- 
tion. Certainly  all  who  put  A  at  its  point  understand  the 
matter.  Then  put  A  at  its  point  on  the  board.  Some  inches 
away  from  the  first  arrow  draw  a  second,  making  an  angle 
with  A,  and  when  pupils  have  done  likewise,  ask  for  a  name. 
Put  B  at  its  point  and  draw  another  arrow  in  the  same  direc- 
tion some  feet  away,  and  name  as  before.  So  continue  until 
you  have  on  the  board  and  the  pupils  have  on  their  pads  a 
number  of  arrows  in  each  of  a  number  of  directions.  Ask 
pupils  which  direction,  B  or  C,  differs  more  from  A.  After 
a  little  exercise  in  this  matter,  ask  pupils  how  to  make  it  evi- 
dent that  C  differs  more  from  A  in  direction  than  B  does. 
Some  pupil  will  suggest  taking  a  point  and  drawing  three  ar- 
rows in  directions  of  A,  B,  and  C.  Continue  this  exercise 
until  pupils  are  familiar  with  the  idea  of  difference  of  two 
directions  and  begin  to  call  it  "angle." 

Ask  all  your  pupils  to  point  at  you,  and  then  ask  them  to 
think  that  you  are  pointing  at  every  one  of  them,  and  write 
up  facts  as  to  resemblances  and  differences  of  directions. 
Some  will  use  the  word  "  opposite."  Some  will  say  :  "  You  are 
pointing  just  the  other  way  from  that  in  which  I  am  point- 


PRACTICAL   LESSONS.  67 

ing."  Use  the  words  "  opposite  directions,"  and  apply  them 
to  the  case  in  hand. 

Place  four  boys,  A,  B,  C,  and  D,  in  different  parts  of  the 
room ;  ask  A  and  B  to  point  at  each  other,  and  ask  C  to 
point  in  a  direction  opposite  to  the  direction  in  which  A  is 
pointing,  and  D  to  point  in  direction  opposite  to  the  one  in 
which  B  is  pointing.  Then  ask  some  pupil  to  use  a  pointer 
and  point  in  a  direction  midway  between  these  opposite 
directions.  He  will  probably  try  to  get  midway  between  the 
four  boys,  but  if  you  have  the  four  boys  properly  located  he 
will  find  that  impossible.  Then  write  on  the  board  the  two 
propositions,  viz:  "Place  your  person  midway  between  the 
pupils,"  and  "  point  in  a  direction  midway  between  the  oppo- 
site directions."  Ask  for  resemblances  and  differences.  When 
satisfactory  answers  are  received,  ask  the  pupils  at  their  seats, 
without  leaving  their  seats,  to  point  in  a  direction  midway 
between  the  opposite  directions.  A  number  will  do  this 
for  you  without  delay,  and  if  you  give  out  six  pointers,  you 
will  have  six  different  directions  which  are  midway  between 
the  given  opposite  directions.  Then  take  four  points  on  the 
blackboard  at  considerable  distances  from  each  other,  name 
them  A,  B,  C,  and  D.  Ask  some  pupil  to  put  an  arrow  with  its 
point  at  A ;  a  second  pupil  to  put  an  arrow  with  its  point  at 
B,  pointing  in  opposite  directions  from  that  at  A;  a  third 
pupil  to  place  an  arrow  with  its  point  at  C,  pointing  in  oppo- 
site direction  from  the  arrow  at  A;  and  likewise  place  an 
arrow  at  D  in  the  opposite  direction  from  that  at  B.  Let 
pupils  write  up  ivhat  and  how,  and  then  give  out  pointers  to 
different  pupils  to  give  direction  midway  between  these  oppo- 
sites,  and  then  let  a  number  of  pupils  draw  arrows  at  differ- 
ent points,  E,  F,  G,  etc.,  pointing  in  directions  midway  be- 
tween the  opposites  that  are  on  the  board.  Then  the  pupils 
are  prepared  for  the  name,  7ight  angle. 

With  this  unit,  they  should  be  required  to  actually  meas- 
ure a  number  of  acute  and  obtuse  angles.  This  measurement 
of  angles  with  a.  right  angle  for  a  unit  is  readily  taught  by 
the  methods  of  this  Monograph. 


68  PEDAGOGICS. 

Ask  the  pupils  to  draw  a  triangle  like  one  on  the  board, 
which  the  teacher  makes  obtuse  angled.  Ask  the  pupils  to 
separate  it  into  its  parts.  The  average  pupil  will  readily  find 
the  six  parts.  Ask  him  to  construct  another  triangle  with 
any  three  of  the  six  parts.  He  will  probably  not  select  the 
three  angles ;  if  he  does,  resemblances  and  differences  will 
disclose  the  facts  in  the  case,  as  it  does  whatever  three  parts 
he  may  select.  Then  let  him  select  three  other  parts,  and 
construct  another  triangle,  and  so  continue ;  the  teacher 
always  asking  for  resemblance  and  difference  between  the 
resulting  triangle  and  the  one  he  started  with,  until  he  is  per- 
fectly familiar  with  the  evident  principle  in  the  case.  Of 
course,  when  he  happens  to  select  two  sides  and  an  angle 
opposite  one  of  the  sides,  he  may  have  a  result,  well  known 
to  the  reader,  which  must  be  treated  as  correct  principles  in 
teaching  demand. 

With  older  pupils  it  requires  some  four  weeks,  an  hour 
each  day,  to  do  this  work  well ;  with  younger  pupils,  some 
ten  weeks.  Older  pupils  at  this  stage  ought  to  have  now  and 
then  a  proposition  to  study,  as  found  in  the  average  geometry 
of  the  day.  The  teacher  ought  to  write  on  the  board  such  a 
demonstration  for  the  younger  pupils  to  copy  on  their  pads 
and  study  under  the  teacher's  directions,  with  the  what,  how, 
and  why  while  writing  the  propositions. 

It  seems  sure  that  all  of  geometry  can  be  taught  after  the 
same  plan,  but  it  has  been  found  that  pupils  use  books  in  a 
satisfactory  manner  after  this  period. 

Note.— The  observant  teacher  will  perceive  that  all  the  principles  of  arith- 
metic (pages  24  and  25)  apply  to  geometry. 

Principles  (13)  and  (14)  in  geometry  take  the  following 

forms,  viz : 

AocB).-.A--A'  =  B--B'.-. 
A'oc  B'  f        A    :   A'  =  B   :    B'. 


and 


Boc:^I..B^B'  =  C'--C. 


B'oc  ^1         B   :    B'  =  C   :   C. 


PRACTICAL  LESSONS. 


69 


Also  an  additional  2>riiiciple   appears  in  this  connection, 
which  may  be  generically  stated  thus : 


r  B  1 

C 


Aoc^  J,  } 


etc. 

__L 
D 


E 

^etc.  > 


*       B  Cetc.       ^ 

A  =  -— — X  (some  constant^). 

D   E  etc. 


'This  constant  must  be  used  in  the  generic  expression. 

1 


EDUCATION  OF  CHARACTER, 


What  a  man  does  once  under  given  circumstances  does  not 
proclaim  his  character ;  but  if  he  does  any  one  thing  repeat- 
edly under  like  circumstances,  that  one  act  may  be  regarded 
as  a  phenomenon  of  his  character.  If  a  boy  habitually  comes 
into  the  school-room  when  the  bell  rings,  we  credit  him  with 
promptness  as  one  element  of  his  character.  And  so,  every 
habit  of  the  individual  is  a  mark  of  his  character. 

If  a  man  gives  habitually,  as  calls  are  matle  upon  him,  he 
must  be  credited  with  liberality.  His  failing  to  give  at  any 
one  time  does  not  invalidate  the  previous  estimate.  More- 
over, a  man  does  not  sit  in  judgment  upon  his  own  acts  ;  the 
standard  of  right  action  is  fixed  by  public  opinion  ;  it  changes 
from  age  to  age.  Just  now,  for  us,  it  has  its  foundation  in 
the  precepts  of  Christ,  and  he  who  does  his  duty  faithfully 
must  conform  his  teaching  to  that  standard.  Now,  do  not 
these  facts  lead  inevitably  to  the  conclusion  that  he  who  suc- 
ceeds in  molding  character  aright  must  fix  habits  of  action 
that  to  the  world  indicate  excellence  in  character? 

A  man's  whole  life  is  spent  in  accomplishing  ends  through 
means.  If  all  the  ends  he  seeks  are  good,  and  all  the  means 
employed  by  him  are  right,  then  his  character  is  perfect. 

Now,  certain  ends,  as  food,  clothing,  etc.,  demand  a  large 
share  of  every  one's  energies  and  time  for  their  accomplish- 
ment. Satisfying  them  becomes  in  fact  the  business  of  his 
life.  For  gaining  these  constant  ends,  by  comparing  the 
means  that  he  has  from  time  to  time  employed,  he  assimilates 
certain  principles.  These  laws  as  constant  means  control  to 
a  great  extent  his  habits  and  develop  his  character. 

The  ends  one  shall  seek  are  suggested  by  his  feelings ;  these 
command  his  Will  and  it  obeys  ;  he  seeks  the  suggested  ends; 


EDUCATION    OF    CHARACTEK.  "Tl 

his  experunces  commence.  Certain  ends  acconipii.^hed''0»* 
means  employed  bring  him  into  conflict  with  his^environment, 
and  he  experiences  pain  where  he  anticipated  pleasure.  Now 
his  Intellect  begins  its  benign  work  ;  he  makes  a  rule  for  him- 
self in  each  case  of  experienced  pain ;  his  Intellect  gives  a 
lesson  to  his  emotional  nature. 

But  Emotion  again  prompts  him,  and  again  his  Will  obeys. 
Again  his  environment  inflicts  pain,  and  as  his  promptings  must 
have  been  stronger  than  at  first  to  overcome  his  determina- 
tion, so  his  pen-istence  is  greater.  His  Intellect,  this  time 
starting  from  principle,  can  make  its  lesson  more  forcible. 

As  often  as  this  conflict  may  be  waged,  just  so  often  is  the 
end  the  same.  The  determination  dictated  by  the  intellect 
will  become  getieric,  and  a  habit  be  born. 

Passion,  in  some  cases,  may  temporarily  or  permanently 
control  the  Will,  but  the  individual  ever  remembers  the  les- 
sons of  his  Intellect,  and  despises  himself  when  disobeying  its 
mandates. 

Those  habits  which  are  acquired  through  a  triumph  of 
the  intellect  over  the  emotional  nature  are  good,  because  they 
are  founded  on  truth,  the  assimilation  of  which  is  the  work 
proper  of  the  intellect.  Bad  habits  are  acquired  by  obeying 
the  emotional  nature.  Such  are  observed  to  prevail  with 
peoples  and  individuals  whose  intellects  are  naturally  weak, 
or  who  have  been  so  unfortun  ite  as  to  have  had  meager  intel- 
lectual training. 

The  problem  to  be  solved  by  the  teacher  or  the  parent 
who  undertakes  to  educate  the  character  of  a  young  person 
is :  To  prepare  him  to  so  act  as  to  be  in  harmony  with  an  ever- 
varying  environment. 

The  pupil's  character  will  be  educated  aright  if  he  acquires 
good  habits  and  drops  such  bad  habits  as  he  may  have  fallen 
into.  Good  habits  are  at  war  with  bad  habits,  and,  if  the 
teacher  will  but  re-enforce  the  good  in  the  struggle,  their  vic- 
tory will  be  more  certain. 

Fault-finding,  lecturing,  and  scolding  are  among  the  worst 


<  J  PEDAGOGICS. 

ti.eans  a  teacher  can  employ  to  cure  bad  habits,  for  the  very 
apparent  reason  that  the  pupil  does  not  realize  that  the  fault- 
finding is  directed,  not  at  his  person  but  at  his  habit ;  he  infers 
that  his  teacher  does  not  love  hirn,  and  this  impression  puts 
the  teacher  outside  of  the  pupil's  environment  for  good,  and 
makes  his  influence  a  nullity  or  an  actual  evil. 

Good  habits  must  be  cultivated  systematically,  and  herein 
lies  the  solution  of  the  problem.  What  are  the  elements  of 
that  solution,  what  are  the  laws  that  should  govern  the 
teacher?  The  objective  point  for  the  teacher  is  to  lead  the 
pupil  to  form  generic  determinations.*  As  has  already  been 
indicated,  the  making  of  these  generic  determinations  are  the 
turning-points  in  life.  Victor  Hugo  said :  "A  tuft  of  sod 
against  which  a  soldier  rests  his  heel  in  the  conflict  may  de- 
cide the  fate  of  a  nation." 

So,  a  little  thing  may  often  mar  or  make  a  character.  A 
''  word  in  season  "  by  his  teacher  may  turn  a  boy  from  the 
downward  path,  or  by  a  single  mistake  in  judgment  that  teach- 
er may  start  him  on  the  road  to  ruin.  Every  person  of  mature 
years  can  recall  many  such  turning-points  in  his  life.  They 
abide  in  memory  with  peculiar  force,  because  each  of  them 
marks  a  triumph  of  temptation,  or  a  victory  for  truth,  the 
very  sap  upon  which  the  intellect  feeds. 

Now,  can  these  determinations  and  their  resulting  good 
habits  be  made  to  come  to  pass  with  any  certainty,  or  must 
we  regard  them  as  providential  entirely? 

As  a  teacher's  wisdom  may  decide  in  answering  this  ques- 
tion, so  will  his  practice  be  shaped.  If  he  believes  that  Provi- 
dence alone  determines,  he  will  leave  the  issue  in  His  hands ; 
if  the  teacher  believes  that  he  is  one  instrument  of  Providence 
for  the  well-being  of  his  pupil,  he  will  feel  called  on  to  work 
as  well  as  pray. 

'^  By  a  generic  determination  is  meant  a  resolntion  fo  act  at  all  times  and  in 
all  places  according  to  the  dictates  of  the  law  conceived  to  be  proper.  There  is 
a  difference  between  determining  to  quit  wine  and  determining  to  quit  all  in- 
toxicating liquors;  between  resolving  to  be  prompt  to-morrow  and  to  be 
prompt  ev'3ry  day:  the  one  is  particular,  the  other  generic. 


EDUCATION    OF    CHARACTER.  73 

There  are  certain  conditions  in  this  problem  df  •(^duxjalkig 
character  which  are  constant.  Success  can  in  no  case  be  cer- 
tain unless  these  are  satisfied,  viz: 

1.  Every  pupil  has  an  environment  which 
differs  more  or  less  from  that  of  every  other 
pupil. 

2.  The  pupil's  intellect  is  a  part  of  his  own 
environment. 

3.  The  teacher  must  know  the  environment  of 
each  pupil. 

4.  The  teacher  must  know  himself  as  he  is.  * 

The  teacher  must  know  the  particular  environment  of 
eacli  pupil  in  order  to  put  into  it  good  influences  that  are  lack- 
ing, and  to  take  out  bad  influences  that  are  present. 

What  will  produce  good  results  with  one  will  often  pro- 
duce the  contrary  results  with  another;  what  is  needed  to 
influence  one  is  already  in  another's  environment,  or  if  put 
there  would  do  no  good.  A  boy  who  loves  music  can  be 
benefited  by  it ;  one  who  loves  it  not  fails  to  be  influenced 
by  it.  The  '*  I  do  not  like  that"  of  a  person  that  he  respects 
causes  a  child  to  pause  ;  where  respect  is  wanting  he  does  not 
often  heed  it.  A  teacher  once  had  occasion  to  lecture  a  lad 
about  something  he  had  done.  "  I  wish  you  would  ask  your 
Uncle  Will  what  he  thinks  about  such  an  offense,"  he  ven- 
tured as  a  feeler.  The  boy  responded,  with  a  blush,  "I  will, 
but  don't  you  tell  him  first.  Let  me  tell  him."  That  teacher 
had  found  a  new  element  to  put  in  that  boy's  environment; 
his  desire  to  retain  his  Uncle  Will's  love  became  a  disciplinary 
force  with  the  boy  from  that  day. 

Tom  Brown  needed  the  gentle  influence  of  the  pastor's 
son  upon  his  rugged  nature;  he  needed  care  as  a  burden  in 
his  life  to  discipline  him  ;  the  little  timid  boy  needed  a  manly 

*  This  condition  can  be  understood  by  reading  carefully  Christ's  qualifica- 
tions as  a  teacher  as  outlined  in  Hebrews  ii.  17-18;  iv,  15,  and  those  of  Paul  in 
1st  Corinthians,  ix,  19  to  22. 


74  PEDAGOGICS. 

protector;  the  wise  Arnold  brought  them  together.  It  was 
a  simple  thing  to  do,  but  it  produced  a  great  change  in  the 
life  of  each.  This  story  of  Tom  Brown  at  Rugby,  however 
much  a  fiction,  tells  some  wonderful  facts  in  character  educa- 
tion. 

That  every  pupil's  intellect  is  a  part  of  his  environment 
for  good  is  apparent  from  what  has  been  said  above  in  refer- 
ence to  good  habits  and  the  conflict  antecedent  to  their  form- 
ation. 

That  every  pupil  has  a  different  environment  or  total  of 
influences  is  sure.  One  has  a  father,  another  has  not;  one 
has  an  Uncle  Will,  another  has  an  Uncle  Ben;  one  reads 
good  books,  another  nothing ;  one  is  a  prey  to  certain  vices, 
another  is  free  from  them  ;  one  comes  from  a  home  where 
religion  has  sway,  another  knows  nothing  of  it. 

No  two  individuals  are  alike,  because  no  two  have  the  same 
environment. 

Stupendous  is  the  task  upon  the  teacher  of  undertaking  to 
train  the  characters  of  forty  children,  each  having  a  different 
environment;  great  is  his  responsibility,  but  he  should  not 
shrink  from  the  one  or  be  appalled  at  the  other.  Much  can 
be  done  by  him  in  improving  the  environments  of  the  several 
children  in  his  charge  ;  much  can  be  done  by  him  in  educating 
their  characters  if  he  will  but  systematize  his  work. 

The  same  postulates  apply  in  educating  the  character,  as 
are  given  in  a  former  section  to  govern  the  teacher  in  train- 
ing the  intellect.* 

In  arranging  his  "  wholes"  for  lessons  in  character  a  little 
reflection  will  show  the  teacher  that  they  must  be  compre- 
hensive enough  to  cover  all  grades  of  character-development 
in  the  class.  That  this  is  possible  with  any  class  will  be  appar- 
ent when  one  reflects  that  there  is  rarely  very  great  dissimi- 


*  Postulate  II  will  not  be  satisfied  in  a  character-lesson  unless  the  pupil's 
intellect,  dominating  his  will,  is  one  factor  of  his  environment.  He  theu  be- 
comes in  truth  "self-active;"  i.  e.,  he  completes  the  "whole"  through  which 
he  makes  a  generic  determination. 


EDUCATION  OF  CHARACTER.  75 

larity  in  their  individual  environments.  These  "wholes"  must 
always  be  made  up  in  part  of  material  in  the  actual  environ- 
ment of  the  pupil,  and  the  matter  of  them  must  be  so  pre- 
sented as  to  cause  each  one  to  make  a  personal  application  of 
the  matter  presented  to  his  own  conduct;  this  is  best  done  by 
a  hypothetical  talk,  as  will  be  illustrated  later. 

From  what  has  been  said  above,  the  following  principles 
for  the  guidance  of  the  teacher  may  be  inferred : 

I.  *'  Wholes  "  are  identical  only  so  far  as  their 

parts  are  the  same. 

II.  A  "  whole  "  is  made  up  of  parts  related. 

III.  Varying  the  parts  varies  the  "whole."* 

* 

But  a  grave  responsibility  rests  upon  the  teacher  who  con- 
structs "wholes"  to  influence  tlie  life  of  a  child.  Wisdom 
has  been  defined  to  be,  "The  use  of  the  best  means  for  the 
attainment  of  the  best  ends."  Whewell  says,  "  We  conceive 
prudence  to  be  the  virtue  by  which  we  select  right  means  for 
given  ends,  while  wisdom  implies  the  selection  of  right  ends 
as  well  as  right  means." 

This  being  true,  to  guide  his  pupil  to  the  highest  ultimate 
ends  the  teacher  must  make  his  "wholes"  serve  as  right 
means.     A  fourth  principle  then  may  be  stated,  as  follows : 

IV.  The  best  interests  of  an  individual  are  se- 
cured in  the  attainment  of  the  best  "wholes" 
possible. 

An  evident  corollary  of  this  principle  is : 


*  One  will  not  appreciate  at  a  casual  reading  that  these  principles  lie  at  the 
very  foundation  in  character  training.  The  lapse  of  time,  ihe  influence  of  the 
weather,  the  incidental  influence  of  what  has  happened  the  same  day,  a  thou- 
sand little  influences  that  are  potent  in  every  "  whole  "  presented  by  a  teacher 
make  it  necessary  to  regard  the  truths  asserted  above  at  all  times  and  in  every 
lesson.  One  may  attempt  to  do  to-morrow  or  next  year  what  he  has  success- 
fully done  to-day;  but  if  he  copies  himself  he  will  fail.  The  day,  the  hour, 
the  pupils,  and  he  himself  are  all  changed  elements  in  the  "  whole." 


76  PEDAGOGICS. 

V.  The  best  interests  of  his  associates  are  the 

]best  interests  of  an  individual. 

The  mind  of  man  has  three  distinguishable  yet  not  separ- 
able elements,  viz.,  latellect,  Emotion  (sensibility),  and  Will. 
These  three  in  their  functions  are  similar  to  the  three  Depart- 
ments of  our  Government.  Will  is  Executive,  Emotion  is  Leg- 
islative, and  Intellect  Judicial. 

The  mind,  through  Emotion,  by  means  of  conscious  resem- 
blances and  differences,  discovers  the  concrete  relations  of  sense- 
objects,  and  determines  the  Will. 

The  mind,  through  Intellect,  by  means  of  conscious  re- 
semblances and  differences,  discovers  the  abstract  relations  of 
sense-objects.  It  either  approves  or  declares  null  and  void 
the  work  of  Emotion. 

The  Will,  if  it  be  a  strong  Executive,  obeys  the  mandates 
of  the  Intellect ;  if  it  be  weak  or  corrupt,  it  may  fail  in  its  duty. 

This  analysis  of  the  functions  of  mind  suggests  two  prin- 
ciples which  are  to  the  teacher  alternatives : 

VI.  The  teacher  must  provide  a  "whole"  (envi- 
ronment subject  to  change)  for  his  pupil, 
such  that  the  concrete  and  abstract  relations 
of  the  objects  composing  it  'will  both  act  har- 
moniously in  directing  the  will  of  the  pupil. 

Or,  this  being  impracticable  : 

VII.*  The  teacher  must  try  by  hypothetical  dis- 
course to  secure  in  the  mind  of  the  pupil  a 
corresponding  generic  determination. 

It  must  be  evident  to  the  reader  that  no  one  is  able,  in  any 

*  It  will  hardly  be  possible,  in  any  case,  to  so  arrange  a  school  as  to  keep 
evil  influences  out  of  a  child's  environment  entirely,  yet  what  can  be  done  in 
this  direction  ought  not  to  be  neglected.  Just  so  far  as  is  practicable  Principle 
VI  should  guide  the  teacher,  but  generally  it  will  be  found  that  Principle  VII 
has  also  to  be  applied. 


EDUCATION    OF   CHARACTER.  77 

case  calling  for  action  in  the  now,  to  make  a  law  for  himself 
except  from  his  past  experiences. 

The  education  of  character  consists  largely  in  giving  occa- 
sion for  the  most  varied  possible  experiences  on  the  part 
of  the  pupil.  Hence  the  teacher  must  give  to  his  pupil  the 
most  varied  environments  possible,  or,  as  Postulate  I  requires, 
bring  the  pupil  into  as  many  and  varied  "  wholes  "  as  possi- 
ble, and  by  repetition  of  such  "wholes"  secure  assimilation 
of  desired  principles  and  consequent  good  habits. 

These  considerations  are  of  sufficient  importance  to  sug- 
gest another  principle : 

VIII.  The  teacher  must  familiarize  himself  with 
the  actual  of  his  pupils,  so  that,  as  occasion 
offers,  he  may  extend  and  vary  their  experi- 
ences. 

Now,  as  every  good  habit  results  from  a  triumph  of  the 
intellect  over  the  emotional  nature,  and  as  every  intellect  will 
decide  all  cases  according  to  what  it  thinks  best  for  itself,  and 
as  the  real  best  interests  of  an  individual  are  generally  found 
in  sacrificing  some  of  present  pleasures,  it  becomes  a  difficult 
matter  for  the  teacher  to  secure  the  formation  of  habits  that 
are  verily  good.  He  must,  therefore,  take  as  his  guide  the 
truth  expressed  below,  and  by  repetitions  of  "  wholes,"  based 
upon  their  experiences,  cause  his  pupils  to  assimilate  and 
apply  it  by  practicing  self-sacrifice : 

IX.  The  future  best  interests  of  an  individual 
require,  in    general,   a    present    sacrifice   of 

some  pleasure. 

* 
*     * 

The  teacher  is  one  of  the  most  important  elements  in  the 
changing  environments  of  his  pupil.  While  all  minds  are  alike 
in  kind,  probably  no  two  are  the  same  in  degree.  These  dif- 
ferences in  degree  in  minds  tend  to  produce  differences  in  kind 


78  PEDAGOGICS. 

in  character.     For   these  reasons  another  principle   of  the 
gravest  importance  presents  itself: 

X.  The  teacher  must  treat   every  pupil   in  ac- 
cord with  that  pupil's  character. 

Rules  should  be  as  few  as  possible,  and  should  be  of  that 
kind  alone  which  are  essential  to  secure  unity  and  harmony 
in  the  conduct  of  the  school.  Also  pupils  should  be  taught 
practically  to  understand  that  no  law  applies  to  them  as  indi- 
viduals until  they  have  violated  its  requirements. 

The  tenth  principle,  indeed,  calls  for  the  very  highest 
order  of  tact  on  the  part  of  the  teacher.  If  a  pupil  hears 
the  bell  which  rings  him  to  the  class-room  as  a  tyrannical 
command  which  is  to  be  obeyed  reluctantly,  then  that  pupil 
is  not  entering  into  his  "  whole  "  freely ;  his  is  not  a  self-act; 
while  he  may  enter  the, class-room  and  learn  ever  so  much 
intellectually,  he  has  not  completed  his  "whole,"  and  his 
character  is  not  being  educated;  the  teacher  is  failing  with 
that  pupil,  and  must  continue  to  fail  until  in  some  way  he  can 
bring  the  pupil  into  a  "  better  mind."      ^ 

If,  however,  the  pupil  hears  that  bell  as  a  clock  ringing 
out  the  time  of  day  when  duty  calls  him  to  work,  and  goes 
gladly  to  his  class,  then  he  has  entered  into  his  "  whole;"  his 
character  is  being  educated ;  the  teacher  is  succeeding  with 
him. 

However  much  importance  may  be  properly  attached 
to  the  education  of  the  mind,  yet  none  the  less  importance 
must  be  attached  to  the  healthful  education  of  the  body.  It 
does  not  seem  that  a  sound  mind  can  coexist  with  an  unsound 
body.  A  differentiation  of  functions  for  individuals  or  for 
classes  in  society  which  extends  to  the  destruction  of  a  health- 
ful equilibrium  of  the  physical  structure  or  mental  structure 
of  the  individual  can  not  be  conceived  to  be  the  best  in- 
terests of  society.     Hence  the  principle : 


EDUCATION  OF  CHARACTER.  79 

XI.  The  teacher  must  ever  attend  to  the  health- 
ful development  of  the  body  of  the  pupil. 

* 

An  education  which  fails  to  give  the  body  of  the  individ- 
ual as  an  instrument  into  the  possession  of  the  mind  is  sadly 
out  of  joint  with  a  healthful  natural  economy.  A  truly  edu- 
cated mind  is  ever  using  its  body  as  an  instrument  in  a  strug- 
gle with  the  environment  of  the  now.  The  present  is  the 
womb  of  the  future.  The  dreamer  of  a  future  which  is  not 
founded  on  the  present  is  the  slave  of  his  body.  For  such 
a  being  the  final  wreck  of  hope  is  certain.  To  destroy  is  not 
to  establish.  It  is  the  pupil's  mind,  not  the  teacher's,  which 
must  control  freely  the  bo<^ly  of  the  pupil.  The  tom-cat-like 
teacher  of  mice-like  pupils  can  never  educate  the  young  cor- 
rectly. Happy  the  pupil  wiiose  teacher  can  steer  him  clear 
of  both  the  Scylla  of  license  and  the  Charybdis  of  slavery  in 
his  education.     Hence: 

XII.  The  true  teacher  must  ever  have  regard  for 
the  establishment  of  such  an  environment  as 
.will  demand  every  day  the  exercise  of  the 
body  as  an  instrument  of  the  mind.* 

*  *  * 

It  will  be  observed,  on  reflection,  that  in  all  correct  teach- 
ing, in  mathematics,  language,  and  the  like,  the  pupil  is  him- 
self ever  entering  as  a  part  of  every  "whole,"  and  that 
hence  in  all  proper  education  the  character  of  the  pupil  is 
being  educated.  In  an  important  sense  assimilation  means 
appropriation  of  the  objective  whole  in  a  subjective  state. 
The  pupil  who  is  so  taught  as  to  form  the  habit  of  obedience 
to  assimilated  principles  in  sciences  is  thus  forming  the  habit 
of  obedience  to  every  principle  of  every  kind. 

Therefore: 

*The  truth  announced  in  this  principle  is  Nature's  demand  for  the  intro- 
duction of  manual  training  into  schools. 


80  PEDAGOGICS. 

XIII.  The  end  of  all  true  teaching  is  the  educa- 
tion of  character. 

DIFFERENTIATION   IN    CHARACTER. 

Between  boys  and  girls  there  are  differences  in  character 
which  become  more  marked  when  they  become  men  and 
women.  These  are  brought  about  by  the  promptings  of 
desires  seeking  ends,  thus  giving  birth  to  habit*,  good  or  bad. 

As  the  ends  apt  to  become  constant,  which  are  sought  by 
the  two  sexes,  are  necessarily  different,  a  difference  in  char- 
acter is  to  be  expected.  But  the  difference  is  not  so  great  as 
to  make  it  inexpedient  to  educate  the  sexes  together,  as  was 
once  the  rule. 

However  desirable  it  may  be  (and  it  would  be  better)  to 
have  separate  schools  for  boys  and  girls,  it  has  been  fbuiid 
impracticable,  and  will  probably  remain  so  for  some  time,  to 
have  other  than  mixed  schools  for  primary  and  secondary 
grades. 

The  general  problem,  then,  of  educating  character  must 
be  complicated  necessarily  by  the  primal  differentiation,  male 
and  female.  What  is  said  further,  therefore,  should  be  under- 
stood as  drawn  from  resemblances  and  differences  in  conduct 
without  reference  to  sex. 

Character  manifests  itself  in  habits;  and,  as  persons  are 
observed  to  have  many  or  few  habits,  so  they  need  to  be  clas- 
sified as  to  character  according  to  these  resemblances. 

Active  and  passive  are  suggestive  terms  by  which  to  character- 
ize these  two  types  of  character,  and  will  be  used  in  this  discus- 
sion to  refer  respectively  to  persons  of  many  and  of  few  habits. 

Of  persons  who  have  developed  or  are  developing  active 
characters,  some  incline  to  contract  good  habits,  while  others 
heedlessly  drift  into  bad  habits. 

Positive  and  negative  are  terms  that  will  be  used  in  this  discus- 
sion to  name  characters  as  they  may  be  differentiated  by  this  ob- 
servation. 


EDUCATION   OF   CHARACTER. 


81 


Of  persons  who  have  few  habits — passive  in  character — 
some  are  observed  to  tend  toward  the  positive,  others  toward 
the  negative,  \yhile  a  few  can  not  be  said  to  exhibit  any  ten- 
dency whatever. 

These  three  classes  of  characters  will  be  spoken  of  as  passive- 
positive,  passive-negative,  and  typical-passive. 

For  the  convenience  of  the  reader  the  full  classification  is 
here  shown : 

f       Positive, 
I    (good  habits). 

I      Negative, 
1^  (bad  habits). 


Character. 


(^  Passive. 


Passive-positive, 
(tends  to  good  habits). 

Passive-negative, 
(tends  to  bad  habits). 

Typical -passive, 
(no  tendency  observed). 


Somewhere  in  one  of  the  classes  named  every  boy  or  girl 
entering  school  finds  his  or  her  place.  Each  type  of  charac- 
ter demands  an  appropriate  general  manner  of  treatment. 
"To  treat  all  alike"  is  a  principle  that  defeats  the  end  of 
educating  character,  whatever  it  may  accomplish  in  securing 
good  order  and  no  complaints. 

It  follows,  then,  that  a  teacher,  to  succeed,  must  know  his 
children,  i.  e.,  knoiv  their  habits,  and  apply  the  proper  treat- 
ment to  have  habits  continued  if  good,  to  change  them  if  bad, 
and  to  induce  habits  if  they  are  lacking. 

If  the  child  is  positive  in  character,  it  is  because  he  has  had 
kind  and  wise  treatment.  Such  g0v>d  habits  as  he  has  ac- 
quired were  l)Drn  of  his  trying  to  make  others  happy,  and 
have  thus  far  been  fostered  by  having  his  efforts  appreciated, 

6 


82  PEDAGOGICS. 

As  a  rule,  such  children  must  be  treated  in  school  exactly  as 
they  have  been  treated  at  home. 

This  class  of  children  bring  apples  to  the  teacher,  or  offer 
parts  of  their  lunch  to  him,  or  volunteer  to  help  him ;  if  their 
little  courtesies  are  not  appreciated  and  recognized,  they  will 
graduUy  discontinue  them,  and  be  injured  in  character  by  the 
heedless  behavior  of  the  teacher. 

If  a  child  is  negative  in  character,  he  has  been  treated 
unwisely  at  home.  Too  much  has  been  done  for  him  by  his 
parents  or  elders ;  not  cares  enough  have  been  put  upon  him  ; 
his  selfish  desires  have  been  too  much  gratified ;  he  has  heard 
too  much  of  the  evil  and  too  little  of  the  good  that  he  and 
others  do ;  he  has  been  lectured  too  much ;  or  his  efforts  to 
do  right  (every  child  makes  them)  have  not  been  observed 
and  commended.  This  class  of  children  are  at  "  outs"  with 
every  thing  that  offers  to  restrain  them  in  their  desires ;  they 
enter  school  with  feelings  toward  the  teacher  similar  to  those 
of  a  criminal  toward  his  jailer. 

The  proper  line  of  treatment  for  one  of  this  class  is  to 
find  out,  first,  how  he  expects  you  to  do  when  he  tries  you,  and 
then  disappoint  him  by  doing  some  other  way.  He  m.ust  be 
made  to  experience  pain  for  his  misdeeds.  Now,  it  he  expects 
a  whipping,  he  will  take  it  and  exult  in  his  victory,  because 
he  has  steeled  himself  to  bear  it ;  but  if  some  other  punish- 
ment is  given  it  breaks  him  up. 

Punishments  ought  to  be  in  the  nature  of  effects  from 
causes.  This  makes  them  a  part  of  the  environment  of  a 
child,  and  hence  they  contribute  to  his  education  in  right 
doing.  But  setting  traps  and  watching  them  for  victims  is  not 
the  province  of  the  teacher  who  wishes  to  educate  character. 

Negative  characters  need  to  be  kept  busy;  cares  must  be 
put  upon  them ;  they  must  be  brought  into  environments  that 
will  cause  them  in  a  natural  way  to  desire  to  do  right.  They 
expect  the  teacher  to  watch  them ;  hence  he  must  not  watch 
them.  They  have  not  been  trusted  by  others  ;  he  must  trust 
them. 


EDUCATION   OF   CHARACTER.  88 

Children  who  are  passive  in  character  are  usually  made  so 
by  actual  cruelty ;  by  repression  of  their  activities,  which 
amounts  to  cruelty  ;  by  being  overtasked  physically  ;  by  being 
allowed  to  indulge  their  appetites  to  excess,  or  by  being 
allowed  to  contract  unhealthy  habits. 

Such  children  are  listless  at  play  and  inattentive  at  les- 
sons ;  are  slow  and  awkward  in  movement,  and  imitators  of 
others  in  every  thing ;  they  are  easily  persuaded  and  easily 
influenced;  negatives  make  cat's-paws  of  them. 

The  proper  treatment  of  them  consists  (1)  in  making 
them  active,  and  (2)  in  pursuing  the  line  of  treatment  appro- 
priate to  the  tendencies  they  may  manifest. 

"Making  them  active"  can  be  accomplished,  generally, 
through  some  study  or  play  that  will  interest  them.  Try  the 
whole  range  of  things  done  at  school  till  the  pupil's  natural 
bent  is  found.  Give  him  free  run  in  this  pursuit  until  he  has 
acquired  independent  action.  By  degrees  he  can  be  led  to 
take  interest,  and  become  active  in  other  studies  or  plays. 

Drawing,  modeling,  and  making  things,  if  introduced  into 
the  regular  curriculum,  would  save  m:iny  a  passive  child  that 
schools,  as  now  organized,  fail  to  interest  and  educate. 

The  foregoing  analysis  and  remarks  have  been  intended  to 
assist  the  teacher  as  far  as  possible  in  systematizing  his  inter- 
course with  those  under  his  charge.  If  he  will  observe  the 
habits  of  his  pupils  he  can,  in  a  few  days,  or  weeks  at  most, 
classify  them  as:  Positive,  negative,  passive-positive,  passive- 
negative,  and  typical-passive. 

This  classification  made,  when  a  pupil  tells  you  something, 
or  asks  a  favor,  or  is  observed  to  do  a  willful  act,  it  assists  in 
determining  promptly  what  to  do  for  his  good. 

A  little  boy,  for  illustration,  tells  you  that  Johnny  has 
taken  his  ball.  If  both  are  negatives,  you  know  at  once  that 
it  was  an  act  of  reprisal.  If  Johnny  is  a  positive,  you  know 
he  has  a  claim  on  the  ball  that  he  thinks  is  good.  If  the 
boy  who  complains  is  a  positive  and  Johnny  is  a  negative,  you 
know  it  is  either  a  robbery  or  a  case  of  plaguing.     If  Johnny 


84  (         PEDAGOGICS. 

is  a  passive,  you  should  investigate  the  case  fully  in  order  to 
reclassify  him.  If  the  complainant  is  a,  passive,  you  know  he 
needs  protection. 

No  child  is  positive  in  every  habit,  neither  is  any  one  nega- 
tive entirely.  Care  must  be  taken,  therefore,  to  discriminate 
in  every  case  that  arises  as  to  whether  the  parties  concerned 
are  positive  or  negative  as  to  the  habit  involved  in  the  case. 

These  suggestions  have  been  made  to  guide  the  teacher  in 
his  every-day  intercourse  with  his  pupils.  Much  may  be 
done  in  this  way  by  a  wise  teacher,  watchful  of  their  w^elfare, 
to  educate  the  characters  of  his  pupils,  but  no  one  ought  to  be 
satisfied  with  this  alone.  Evil  should  be  attacked  and  dis- 
lodged by  regular  approaches. 

Children  can  be  influenced  by  nature  and  law  in  the  same 
way  as  their  elders  are.  They  are  more  susceptible,  in  fact, 
to  good  influences,  because  they  have  not  become  hardened  in 
wrong-doing;  because  their  passions  have  not  become  impe- 
rious by  long  indulgence,  and  because  their  intercourse  with 
the  world  has  not  yet  made  them  lose  faith  in  promises  not 
backed  up  by  bonds,  and  does  not  yet  incline  them  to  regard 
every  one  who  approaches  them  "  bearing  gifts"  as  a  perfidious 
"Greek."  The  trustfulness  and  faith  of  children  is  great! 
Verily,  he  who  is  given  charge  of  them  has  "  talents  of  gold 
entrusted  to  his  care,"  and  it  behooves  him  not  to  bury  them 
in  the  earth  as  did  the  foolish  servant,  but  to  so  use  them  as 
to  return  them,  increased  in  value,  to  those  who  lent  them. 

When  new  words  are  met  in  the  daily  lessons  whose  mean- 
ings relate  to  ethical  conduct,  especial  pains  should  be  taken, 
as  has  been  illustrated  on  page  53,  that  the  learning  of  the 
new  word  be  accompanied  with  the  formation  of  a  determina- 
tion to  act  in  accordance  with  the  meaning  assimilated. 

HYPOTHETICAL   DISCOUESE. 

Moreover,  at  stated  times,  regular  lessons  should  be  given 
in  the  form  of  "talks"  or  conversations  with  the  children 
about  right  behavior.     At  each  of  these  lessons  the  teacher 


EDUCATION    OF   CHARACTER.  85 

should  make  it  the  objective  point  to  cause  the  children  to 
assimilate  some  moral  principle  of  wide  application. 

To  insure  assimilation  of  the  principle  and  the  consequent 
application  of  it  by  the  children  (see  Postulate  VIII,  page 
20,)  in  their  conduct,  it  is  absolutely  necessary  that  there 
should  have  been  violations  of  it  in  deed  or  thought  in  their  own 
experiences,  and  that  these  violations  should  be  brought  to 
their  memory  by  the  "talk." 

The  bringing  together  of  these  facts  of  their  experience, 
along  with  other  facts  brought  into  the  discourse  by  the 
teacher,  constitutes  constructing  a  "whole"  from  which, 
through  comparison,  the  principle  desired  may  be  assimilated. 

This  discourse,  in  its  subject-matter,  is  apt  to  be  largely 
hypothetical.  It  is  never  advisable  to  allude  to  the  facts  of 
their  experiences,  except  as  a  supposition,  or  as  things  the 
teacher  once  knew  to  happen. 

Any  one  may  become  expert  in  constructing  a  proper 
address  to  inculcate  a  lesson  in  conduct  if  he  will  but  take  the 
pains  to  collect  the  facts  necessary,  and  remember  that  the 
law.  No  one  can  learn  a  truth  by  reading  it  or  hearing  it  unless  he 
knows  it  already  in  its  elements,  is  never  broken  in  the  sphere 
of  moral  any  more  than  in  that  of  intellectual  training. 

A  practical  illustration  is  given  below  of  a  lesson  from 
actual  practice.  The  circumstances  from  which  the  data  were 
derived,  which  served  as  the  "elements  known  already"  by 
the  pupils,  were  as  follows : 

One  Saturday  in  November  the  boys  of  a  school  organized 
a  rabbit  hunt.  About  twenty  were  engaged,  and  four  rabbits 
were  caught.  Those  who  had  caught  the  rabbits  evidenced 
by  their  after-conduct  an  intention  not  to  share  the  prey 
equitably.  Certain  directions  were  given  to  the  cook  by  them 
as  to  how  the  rabbits  were  to  be  dressed,  and  to  the  table-boy 
as  to  where  to  set  the  dishes  the  next  morning.  The  teacher 
had  gathered  all  this  in  the  course  of  the  evening  after  the 
hunt.  He  said  nothing  to  the  boys  at  the  time,  and  only 
interfered  so  far  as  to  disturb  the  table  arrangement  the  next 


86  PEDAGOGICS. 

morning.  The  rabbits  were  served  from  the  head  of  the 
table  along  with  the  steak  and  other  common  dishes.  Some 
surprise  was  apparent  in  the  faces  of  a  few,  but  no  protests 
were  made.  The  rabbit  hunt  and  feast,  in  a  few  days,  were 
no  longer  talked  about. 

Soon  thereafter,  at  chapel  exercises  one  morning,  the  fol- 
lowing diagram  was  placed  on  the  board  by  the  teacher : 


C      men      ~)  C 

<  y  co-operate  < 

(  not  men  \  (^ 


men       )  (   associate 

Animals  ,  ,  ^  , 

herd. 


The  habits  of  wolves  and  other  animals  were  discussed  by 
the  teacher.  The  fact  of  their  co-operation  was  brought  out. 
Its  general  object,  viz.,  to  secure  prey  for  eating,  was  dwelt 
upon.  Their  after-conduct,  seizing  and  devouring  each  for  him- 
self, was  exhibited.  The  fact  that  no  sharing  was  a  principle 
with  wolves  and  other  animals  was  made  prominent.  The  end 
of  their  co-operation  was  shown  to  be  in  the  securing  of  prey. 

The  conduct  of  men  in  co-operating  was  then  taken  up 
and  compared  with  that  of  animals.  A  hunt  of  wolves  had 
been  elaborated,  a  supposed  hunt  of  men  was  narrated  in 
detail.  Their  conduct  when  prey  was  secured  was  contrasted 
with  that  of  the  wolves.  Their  motives  in  co-operating  were 
examined,  and  the  fact  that  their  co-operating  becomes  per- 
manent was  emphasized,  as  also  the  fact  that  sharing  is  a  prin- 
ciple with  men. 

Just  enough  was  said  in  the  discourse  to  insure  the  recall  of 
the  rabbit  episode  in  the  minds  of  the  boys.  No  one  was  per- 
sonally mentioned  ;  no  one  was  criticised ;  no  one  reproved. 

The  discourse  accomplished  the  end  intended,  i.  e.,  it  caused 
the  assimilation  of  a  principle  by  the  boys,  as  was  evidenced 
in  a  few  days  by  remarks  made  in  criticism  of  certain  actions 
questioned  about. 

The  lesson  also  incidentally  served  to  classify  properly 
the  meanings  of  "associate"  and  "herd,"  as  applied  to 
actions  of  animals,  the  one  being  permanent  and  the  other 
temporary  co-operation. 


YB  34908 


L'ZfOZC 


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